Relevant bibliographies by topics / Lie superalgebras

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Lie superalgebras'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 July 2024

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Journal articles on the topic "Lie superalgebras"

1

Pouye, M., and B. Kpamegan. "Extensions, crossed modules and pseudo quadratic Lie type superalgebras." Extracta Mathematicae 37, no. 2 (December 1, 2022): 153–84. http://dx.doi.org/10.17398/2605-5686.37.2.153.

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Extensions and crossed modules of Lie type superalgebras are introduced and studied. We construct homology and cohomology theories of Lie-type superalgebras. The notion of left super-invariance for a bilinear form is defined and we consider Lie type superalgebras endowed with nondegenerate, supersymmetric and left super-invariant bilinear form. Such Lie type superalgebras are called pseudo quadratic Lie type superalgebras. We show that any pseudo quadratic Lie type superalgebra induces a Jacobi-Jordan superalgebra. By using the method of double extension, we study pseudo quadratic Lie type superalgebras and theirs associated Jacobi-Jordan superalgebras.
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Abramov, Viktor. "3-Lie Superalgebras Induced by Lie Superalgebras." Axioms 8, no. 1 (February 6, 2019): 21. http://dx.doi.org/10.3390/axioms8010021.

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We show that given a Lie superalgebra and an element of its dual space, one can construct the 3-Lie superalgebra. We apply this approach to Lie superalgebra of ( m , n ) -block matrices taking a supertrace of a matrix as the element of dual space. Then we also apply this approach to commutative superalgebra and the Lie superalgebra of its derivations to construct 3-Lie superalgebra. The graded Lie brackets are constructed by means of a derivation and involution of commutative superalgebra, and we use them to construct 3-Lie superalgebras.
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3

Sun, Liping, and Wende Liu. "Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields." Open Mathematics 15, no. 1 (November 13, 2017): 1332–43. http://dx.doi.org/10.1515/math-2017-0112.

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Abstract According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras. This is achieved by studying the Hom-Lie superalgebra structures only on their 0-th and (−1)-th ℤ-components.
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Chen, Liangyun, and Daoji Meng. "On the Intersection of Maximal Subalgebras in a Lie Superalgebra." Algebra Colloquium 16, no. 03 (September 2009): 503–16. http://dx.doi.org/10.1142/s1005386709000479.

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The maximal subalgebras and their intersection of a Lie algebra or a Lie superalgebra were studied by Racine, Scheiderer, Elduque, Melikyan, et al. The purpose of the present paper is to continue the investigation in order to obtain deeper structure theorems for Lie superalgebras. We develop the Frattini theory for Lie superalgebras, generalize Barnes's results to Lie superalgebras, and obtain some necessary and sufficient conditions for solvable Lie superalgebras and nilpotent Lie superalgebras. Moreover, some necessary and sufficient conditions for ϕ-free Lie superalgebras and elementary Lie superalgebras are given.
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PEI, YUFENG, and CHENGMING BAI. "BALINSKY–NOVIKOV SUPERALGEBRAS AND SOME INFINITE-DIMENSIONAL LIE SUPERALGEBRAS." Journal of Algebra and Its Applications 11, no. 06 (November 14, 2012): 1250119. http://dx.doi.org/10.1142/s0219498812501198.

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In this paper, we recall the Balinsky–Novikov (BN) superalgebras and revisit the approach of constructing an infinite-dimensional Lie superalgebra by a kind of affinization of a BN superalgebra. As an example, we give an explicit construction of Beltrami and Green–Schwarz–Witten (GSW) algebras from two isomorphic BN superalgebras, respectively, which proves that they are isomorphic as a direct consequence. Moreover, we consider the central extensions of the infinite-dimensional Lie superalgebras induced from BN superalgebras through certain bilinear forms on their corresponding BN superalgebras.
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Elduque, Alberto. "A note on semiprime Malcev superalgebras." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 123, no. 5 (1993): 887–91. http://dx.doi.org/10.1017/s0308210500029553.

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SynopsisPrime Malcev superalgebras over fields of characteristic not two and three have been studied by Shestakov [8]. He obtains the remarkable result that if these superalgebras have a nonzero odd part then they are Lie superalgebras. The main purpose of this note is to extend this result to fields of characteristic three. To this aim, it is enough to use adequately a result of Filippov [3]. Commutative and anticommutative superalgebras will be considered too, showing that they are prime, semiprime or simple as superalgebras if and only if they are as algebras. Finally, some conclusions for finite-dimensional semisimple Malcev superalgebras will be deduced. Any such superalgebra is the direct sum of a semisimple Lie superalgebra and a direct sum of simple non-Lie algebras.
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Sun, Liping, Wende Liu, Xiaocheng Gao, and Boying Wu. "Restricted Envelopes of Lie Superalgebras." Algebra Colloquium 22, no. 02 (April 15, 2015): 309–20. http://dx.doi.org/10.1142/s1005386715000279.

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Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa's theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.
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Guan, Baoling, Xinxin Tian, and Lijun Tian. "Induced 3-Hom-Lie superalgebras." Electronic Research Archive 31, no. 8 (2023): 4637–51. http://dx.doi.org/10.3934/era.2023237.

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<abstract><p>We construct 3-Hom-Lie superalgebras on a commutative Hom-superalgebra by means of involution and even degree derivation. We construct a representation of induced 3-Hom-Lie superalgebras by means of supertrace.</p></abstract>
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9

Huang, Zhongxian. "Conformal Super-Biderivations on Lie Conformal Superalgebras." Journal of Mathematics 2021 (June 2, 2021): 1–9. http://dx.doi.org/10.1155/2021/6624315.

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In this paper, the conformal super-biderivations of two classes of Lie conformal superalgebras are studied. By proving some general results on conformal super-biderivations, we determine the conformal super-biderivations of the loop super-Virasoro Lie conformal superalgebra and Neveu–Schwarz Lie conformal superalgebra. Especially, any conformal super-biderivation of the Neveu–Schwarz Lie conformal superalgebra is inner.
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Yuan, He, and Liangyun Chen. "Lie n superderivations and generalized Lie n superderivations of superalgebras." Open Mathematics 16, no. 1 (March 13, 2018): 196–209. http://dx.doi.org/10.1515/math-2018-0018.

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AbstractIn the paper, we study Lie n superderivations and generalized Lie n superderivations of superalgebras, using the theory of functional identities in superalgebras. We prove that if A = A0 ⊕ A1 is a prime superalgebra with deg(A1) ≥ 2n + 5, n ≥ 2, then any Lie n superderivation of A is the sum of a superderivation and a linear mapping, and any generalized Lie n superderivation of A is the sum of a generalized superderivation and a linear mapping.
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Dissertations / Theses on the topic "Lie superalgebras"

1

Bagnoli, Lucia. "Z-graded Lie superalgebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14118/.

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This thesis investigates the role of filtrations and gradings in the study of Lie superalgebras. The main connections between the Z-grading of a Lie superalgebra and its structure are explained. As an example, the simplicity of the Lie superalgebras W(m,n) and S(m,n) is proved. Finally, the strongly symmetric gradings of length three and five of the Lie superalgebras W(m,n) and S(m,n) are classified.
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Furutsu, Hirotoshi. "Representations of Lie Superalgebras, II." 京都大学 (Kyoto University), 1991. http://hdl.handle.net/2433/168802.

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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである
Kyoto University (京都大学)
0048
新制・課程博士
理学博士
甲第4695号
理博第1293号
新制||理||720(附属図書館)
UT51-91-E66
京都大学大学院理学研究科数学専攻
(主査)教授 平井 武, 教授 池部 晃生, 教授 岩崎 敷久
学位規則第5条第1項該当
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Palmieri, Riccardo. "Real forms of Lie algebras and Lie superalgebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9448/.

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In questa tesi abbiamo studiato le forme reali di algebre e superalgebre di Lie. Il lavoro si suddivide in tre capitoli diversi, il primo è di introduzione alle algebre di Lie e serve per dare le prime basi di questa teoria e le notazioni. Nel secondo capitolo abbiamo introdotto le algebre compatte e le forme reali. Abbiamo visto come sono correlate tra di loro tramite strumenti potenti come l'involuzione di Cartan e relativa decomposizione ed i diagrammi di Vogan e abbiamo introdotto un algoritmo chiamato "push the button" utile per verificare se due diagrammi di Vogan sono equivalenti. Il terzo capitolo segue la struttura dei primi due, inizialmente abbiamo introdotto le superalgebre di Lie con relativi sistemi di radici e abbiamo proseguito studiando le relative forme reali, diagrammi di Vogan e abbiamo introdotto anche qua l'algoritmo "push the button".
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Frisk, Anders. "On Stratified Algebras and Lie Superalgebras." Doctoral thesis, Uppsala : Department of Mathematics, Uppsala university, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7781.

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Duong, Minh-Thanh. "A new invariant of quadratic lie algebras and quadratic lie superalgebras." Phd thesis, Université de Bourgogne, 2011. http://tel.archives-ouvertes.fr/tel-00673991.

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In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan algebras, in the same manner as it was done for singular quadratic Lie algebras and 2-step nilpotent quadratic Lie algebras. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7.
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Duong, Minh thanh. "A new invariant of quadratic lie algebras and quadratic lie superalgebras." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS021/document.

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Dans cette thèse, nous définissons un nouvel invariant des algèbres de Lie quadratiques et des superalgèbres de Lie quadratiques et donnons une étude et classification complète des algèbres de Lie quadratiques singulières et des superalgèbres de Lie quadratiques singulières, i.e. celles pour lesquelles l’invariant n’est pas nul. La classification est en relation avec les orbites adjointes des algèbres de Lie o(m) et sp(2n). Aussi, nous donnons une caractérisation isomorphe des algèbres de Lie quadratiques 2-nilpotentes et des superalgèbres de Lie quadratiques quasi-singulières pour le but d’exhaustivité. Nous étudions les algèbres de Jordan pseudoeuclidiennes qui sont obtenues des extensions doubles d’un espace vectoriel quadratique par une algèbre d’une dimension et les algèbres de Jordan pseudo-euclidienne 2-nilpotentes, de la même manière que cela a été fait pour les algèbres de Lie quadratiques singulières et des algèbres de Lie quadratiques 2-nilpotentes. Enfin, nous nous concentrons sur le cas d’une algèbre de Novikov symétrique et l’étudions à dimension 7
In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan algebras, in the same manner as it was done for singular quadratic Lie algebras and 2-step nilpotent quadratic Lie algebras. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7
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7

Ma, Shuk-Chuen. "Conformal and Lie superalgebras related to the differential operators on the circle /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20MA.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003.
Includes bibliographical references (leaves 148-150). Also available in electronic version. Access restricted to campus users.
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Götz, Gerhard Markus. "Lie superalgebras and string theory in AdS3 x S3." Paris 6, 2006. http://www.theses.fr/2006PA066039.

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McSween, Alexandra. "Affine Oriented Frobenius Brauer Categories and General Linear Lie Superalgebras." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42342.

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To any Frobenius superalgebra A we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer categeory. We define natural actions of these categories on categories of supermodules for general linear Lie superalgebras gl_m|n(A) with entries in A. These actions generalize those on module categories for general linear Lie superalgebras and queer Lie superalgebras, which correspond to the cases where A is the ground field and the two-dimensional Clifford superalgebra, respectively. We include background on monoidal supercategories and Frobenius superalgebras and discuss some possible further directions.
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Gardini, Matteo. "Representations of semisimple Lie algebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9029/.

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La tesi è dedicata allo studio delle rappresentazioni delle algebre di Lie semisemplici su un campo algebricamente chiuso di caratteristica zero. Mediante il teorema di Weyl sulla completa riducibilità, ogni rappresentazione di dimensione finita di una algebra di Lie semisemplice è scrivibile come somma diretta di sottorappresentazioni irriducibili. Questo permette di poter concentrare l'attenzione sullo studio delle rappresentazioni irriducibili. Inoltre, mediante il ricorso all'algebra inviluppante universale si ottiene che ogni rappresentazione irriducibile è una rappresentazione di peso più alto. Perciò è naturale chiedersi quando una rappresentazione di peso più alto sia di dimensione finita ottenendo che condizione necessaria e sufficiente perché una rappresentazione di peso più alto sia di dimensione finita è che il peso più alto sia dominante. Immediata è quindi l'applicazione della teoria delle rappresentazioni delle algebre di Lie semisemplici nello studio delle superalgebre di Lie, in quanto costituite da un'algebra di Lie e da una sua rappresentazione, dove viene utilizzata la tecnica della Z-graduazione che viene utilizzata per la prima volta da Victor Kac nello studio delle algebre di Lie di dimensione infinita nell'articolo ''Simple irreducible graded Lie algebras of finite growth'' del 1968.
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Books on the topic "Lie superalgebras"

1

Gorelik, Maria, and Paolo Papi, eds. Advances in Lie Superalgebras. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02952-8.

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1964-, Zolotykh Andrej A., ed. Combinatorial aspects of Lie superalgebras. Boca Raton: CRC Press, 1995.

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Misra, Kailash, Daniel Nakano, and Brian Parshall, eds. Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/pspum/092.

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Vyjayanthi, Chari, Penkov Ivan B. 1957-, and Block Richard E, eds. Modular interfaces: Modular Lie algebras, quantum groups, and Lie superalgebras. Providence, RI: American Mathematical Society, 1997.

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Eyre, Timothy M. W. Quantum Stochastic Calculus and Representations of Lie Superalgebras. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096850.

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Jakobsen, Hans Plesner. The full set of unitarizable highest weight modules of basic classical Lie superalgebras. Providence, RI: American Mathematical Society, 1994.

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E, Block Richard, Chari Vyjayanthi, Penkov Ivan B. 1957-, and American Mathematical Society, eds. Modular interfaces: Modular Lie algebras, quantum groups, and Lie superalgebras : a conference in honor of Richard E. Block, February 18-20, 1995, University of California, Riverside. Providence, R.I: American Mathematical Society, 1997.

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1949-, Neher Erhard, ed. Locally finite root systems. Providence, R.I: American Mathematical Society, 2004.

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Neher, Erhard. Geometric representation theory and extended affine Lie algebras. Providence, R.I: American Mathematical Society, 2011.

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Etingof, P. I., Alistair Savage, and Mikhail Khovanov. Perspectives in representation theory: A conference in honor of Igor Frenkel's 60th birthday on perspectives in representation theory : May 12-17, 2012, Yale University, New Haven, CT. Providence, Rhode Island: American Mathematical Society, 2014.

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Book chapters on the topic "Lie superalgebras"

1

Berezin, Felix Alexandrovich. "Lie Superalgebras." In Introduction to Superanalysis, 170–228. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-017-1963-6_6.

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Berezin, Felix Alexandrovich. "Lie Superalgebras." In Introduction to Superanalysis, 231–44. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-017-1963-6_7.

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Gorelik, Maria, and Dimitar Grantcharov. "Q-type Lie superalgebras." In Advances in Lie Superalgebras, 67–89. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02952-8_5.

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Penkov, Ivan, and Crystal Hoyt. "Finite-Dimensional Lie Superalgebras." In Springer Monographs in Mathematics, 11–30. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89660-7_2.

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Serganova, Vera. "Representations of Lie Superalgebras." In Perspectives in Lie Theory, 125–77. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58971-8_3.

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Serganova, Vera. "Classical Lie superalgebras at infinity." In Advances in Lie Superalgebras, 181–201. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02952-8_11.

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Zhang, Ruibin. "Serre presentations of Lie superalgebras." In Advances in Lie Superalgebras, 235–80. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02952-8_14.

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Poletaeva, Elena. "On Kostant’s theorem for Lie superalgebras." In Advances in Lie Superalgebras, 167–79. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02952-8_10.

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Mazorchuk, Volodymyr. "Parabolic category O for classical Lie superalgebras." In Advances in Lie Superalgebras, 149–66. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02952-8_9.

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Kulish, P. P. "Quantum Lie Superalgebras and Supergroups." In Research Reports in Physics, 14–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-84000-5_2.

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Conference papers on the topic "Lie superalgebras"

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Chen, Wenjuan. "Intuitionistic Fuzzy Lie Sub-superalgebras and Ideals of Lie Superalgebras." In 2009 International Joint Conference on Computational Sciences and Optimization, CSO. IEEE, 2009. http://dx.doi.org/10.1109/cso.2009.399.

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Khuntia, T. K., R. N. Padhan, and K. C. Pati. "On generalizations of derivations of lie superalgebras." In RECENT TRENDS IN APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0137118.

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FATTORI, DAVIDE, VICTOR G. KAC, and ALEXANDER RETAKH. "STRUCTURE THEORY OF FINITE LIE CONFORMAL SUPERALGEBRAS." In Proceedings of the Fifth International Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702562_0002.

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Mikhalev, Alexander A., and Andrej A. Zolotykh. "Algorithms for primitive elements of free Lie algebras and Lie superalgebras." In the 1996 international symposium. New York, New York, USA: ACM Press, 1996. http://dx.doi.org/10.1145/236869.236929.

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Okubo, Susumu. "Construction of Lie Superalgebras from Triple Product Systems." In HIGH ENERGY PHYSICS: The 25th Annual Montreal-Rochester-Syracuse-Toronto Conference on High Energy Physics MRST 2003: A Tribute to Joe Schechter. AIP, 2003. http://dx.doi.org/10.1063/1.1632172.

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Tolstoy, V. N. "Multiparameter Quantum Deformations of Jordanian Type for Lie Superalgebras." In Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772527_0041.

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Nandi, N., R. N. Padhan, and K. C. Pati. "Isoclinism and factor set in regular Hom-Lie superalgebras." In RECENT TRENDS IN APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0137470.

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TOLSTOY, V. N. "HIDDEN PROPERTY OF EXTENDED JORDANIAN TWISTS FOR LIE SUPERALGEBRAS." In Proceedings of the XI Regional Conference. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701862_0041.

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Kanakoglou, K., C. Daskaloyannis, A. Herrera-Aguilar, H. A. Morales-Tecotl, L. A. Urena-Lopez, R. Linares-Romero, and H. H. Garcia-Compean. "Super-Hopf realizations of Lie superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map." In GRAVITATIONAL PHYSICS: TESTING GRAVITY FROM SUBMILLIMETER TO COSMIC: Proceedings of the VIII Mexican School on Gravitation and Mathematical Physics. AIP, 2010. http://dx.doi.org/10.1063/1.3473853.

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Catto, Sultan, and Vladimir Dobrev. "Effective Supersymmetry Based on SU(3)[sup c]×S Superalgebra." In LIE THEORY AND ITS APPLICATIONS IN PHYSICS: VIII International Workshop. AIP, 2010. http://dx.doi.org/10.1063/1.3460168.

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