Relevant bibliographies by topics / Borel subalgebra

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

Academic literature on the topic 'Borel subalgebra'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Borel subalgebra"

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Luo, Li. "Abelian Ideals with Given Dimension in Borel Subalgebras." Algebra Colloquium 19, no. 04 (2012): 755–70. http://dx.doi.org/10.1142/s1005386712000636.

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A well-known Peterson's theorem says that the number of abelian ideals in a Borel subalgebra of a rank-r finite-dimensional simple Lie algebra is exactly 2r. In this paper, we determine the dimensional distribution of abelian ideals in a Borel subalgebra of finite-dimensional simple Lie algebras, which is a refinement of Peterson's theorem capturing more Lie algebra invariants.
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HUANG, WENXUE. "AN ALGEBRAIC MONOID APPROACH TO LINEAR ASSOCIATIVE ALGEBRAS, II." International Journal of Algebra and Computation 06, no. 05 (1996): 623–34. http://dx.doi.org/10.1142/s0218196796000350.

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Let A be a linear associative K-algebra with unity (LAA), K an algebraically closed field. A K–subalgebra of A containing the unity of A is referred to as a sub-LAA of A. A with respect to the multiplication (respectively, Lie bracket) is an algebraic monoid (respectively, Lie algebra) over K, denoted by AM (respectively, AL). Let G(A) and J(A) denote the unit group of AM and Jacobson radical of A, respectively. The following are proved in this paper. (i) If BM is a Borel submonoid of AM, the Zariski closure of a Borel subgroup of G(A), then B is a sub-LAA of A and [Formula: see text], where [
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Cellini, Paola, and Paolo Papi. "ad-Nilpotent ideals of a Borel subalgebra." Journal of Algebra 225, no. 1 (2000): 130–41. http://dx.doi.org/10.1006/jabr.1999.8099.

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Kumjian, Alexander. "On C*-Diagonals." Canadian Journal of Mathematics 38, no. 4 (1986): 969–1008. http://dx.doi.org/10.4153/cjm-1986-048-0.

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Preface. The impetus for this study arose from the belief that the structure of a C*-algebra is illuminated by an understanding of the manner in which abelian subalgebras embed in it. Posed in its full generality, the question concerning abelian subalgebras would seem impossible to answer. A notion of diagonal subalgebra is, however, proposed which has the virtue that one can associate a “topological”; invariant to the pair consisting of the diagonal and the ambient algebra, from which these algebras may be retrieved.In the setting of von Neumann algebras, the analogous question was addressed
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Nakamoto, Kazunori. "The moduli of representations with Borel mold." International Journal of Mathematics 25, no. 07 (2014): 1450067. http://dx.doi.org/10.1142/s0129167x14500670.

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The author constructs the moduli of representations whose images generate the subalgebra of upper triangular matrices (up to inner automorphisms) of the full matrix ring for any groups and any monoids.
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Cellini, Paola, and Paolo Papi. "Ad-nilpotent ideals of a Borel subalgebra II." Journal of Algebra 258, no. 1 (2002): 112–21. http://dx.doi.org/10.1016/s0021-8693(02)00532-x.

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7

BROWNE, PATRICK J. "ABELIAN IDEALS IN A COMPLEX SIMPLE LIE ALGEBRA." Glasgow Mathematical Journal 59, no. 1 (2016): 255–64. http://dx.doi.org/10.1017/s0017089516000148.

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AbstractIn this note, we give a new simple construction of all maximal abelian ideals in a Borel subalgebra of a complex simple Lie algebra. We also derive formulas for dimensions of certain maximal abelian ideals in terms of the theory of Borel de Siebenthal.
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Panyushev, Dmitri. "Abelian ideals of a Borel subalgebra and root systems." Journal of the European Mathematical Society 16, no. 12 (2014): 2693–708. http://dx.doi.org/10.4171/jems/496.

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Conde, Teresa. "All quasihereditary algebras with a regular exact Borel subalgebra." Advances in Mathematics 384 (June 2021): 107751. http://dx.doi.org/10.1016/j.aim.2021.107751.

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Lian, Haifeng, and Cui Chen. "N-Derivations for Finitely Generated Graded Lie Algebras." Algebra Colloquium 23, no. 02 (2016): 205–12. http://dx.doi.org/10.1142/s1005386716000225.

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The N-derivation is a natural generalization of derivation and triple derivation. Let [Formula: see text] be a finitely generated Lie algebra graded by a finite-dimensional Cartan subalgebra. In this paper, a sufficient condition for the Lie N-derivation algebra of [Formula: see text] coinciding with the Lie derivation algebra of [Formula: see text] is given. As applications, any N-derivation of the Schrödinger-Virasoro algebra, generalized Witt algebra, Kac-Moody algebra or their Borel subalgebra is a derivation.
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Dissertations / Theses on the topic "Borel subalgebra"

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Marko, Frantisek Carleton University Dissertation Mathematics and Statistics. "Quasi-hereditary algebras and their Borel subalgebras." Ottawa, 1996.

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2

Saifi, Halip. "Generalized Borel subalgebras, Verma type modules and new irreducible representations for affine Kac-Moody algebras." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq20582.pdf.

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Nampaisarn, Thanasin [Verfasser], Ivan [Akademischer Betreuer] [Gutachter] Penkov, Alan [Gutachter] Huckleberry, and Vera [Gutachter] Serganova. "Categories O for Dynkin Borel Subalgebras of Root-Reductive Lie Algebras / Thanasin Nampaisarn ; Gutachter: Ivan Penkov, Alan Huckleberry, Vera Serganova ; Betreuer: Ivan Penkov." Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2017. http://d-nb.info/1137054468/34.

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Bowman, John. "Finite-dimensional modules for the quantum affine algebra Uq(g) and its borel subalgebra." 2007. http://www.library.wisc.edu/databases/connect/dissertations.html.

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Yudin, Ivan. "On projective resolutions of simple modules over the Borel subalgebra S^+(n, r) of the Schur algebra S(n, r) for n ≤3." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-000D-F12B-3.

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Yudin, Ivan [Verfasser]. "On projective resolutions of simple modules over the Borel subalgebra S+(n, r) of the Schur algebra S(n, r) for n ≤ 3 / vorgelegt von Ivan Yudin." 2008. http://d-nb.info/988950960/34.

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Book chapters on the topic "Borel subalgebra"

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"Cartan subalgebras, Borel subalgebras and parabolic subalgebras." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-27427-8_29.

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"Borel subalgebras and Dynkin-Kac diagrams." In Graduate Studies in Mathematics. American Mathematical Society, 2012. http://dx.doi.org/10.1090/gsm/131/03.

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Conference papers on the topic "Borel subalgebra"

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Deguchi, Tetsuo. "Generalized Drinfeld Polynomials for Highest Weight Vectors of the Borel Subalgebra of the sl2 Loop Algebra." In Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772527_0011.

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