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Relevant bibliographies by topics / Grassmann-Algebra

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Academic literature on the topic 'Grassmann-Algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Grassmann-Algebra"

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Dacorogna, B., and O. Kneuss. "Divisibility in Grassmann algebra." Linear and Multilinear Algebra 59, no. 11 (2011): 1201–20. http://dx.doi.org/10.1080/03081087.2010.495389.

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Lasenby, A. N. "Grassmann, geometric algebra and cosmology." Annalen der Physik 19, no. 3-5 (2010): 161–76. http://dx.doi.org/10.1002/andp.201010412.

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White, Neil L. "Grassmann?Cayley algebra and robotics." Journal of Intelligent & Robotic Systems 11, no. 1-2 (1994): 91–107. http://dx.doi.org/10.1007/bf01258296.

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Giansiracusa, Jeffrey, and Noah Giansiracusa. "A Grassmann algebra for matroids." manuscripta mathematica 156, no. 1-2 (2017): 187–213. http://dx.doi.org/10.1007/s00229-017-0958-z.

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Nomura, Takaaki. "Grassmann manifold of aJH-algebra." Annals of Global Analysis and Geometry 12, no. 1 (1994): 237–60. http://dx.doi.org/10.1007/bf02108300.

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Nishiyama, Kyo, and Haiquan Wang. "Commutant algebra of superderivations on a Grassmann algebra." Proceedings of the Japan Academy, Series A, Mathematical Sciences 72, no. 1 (1996): 8–11. http://dx.doi.org/10.3792/pjaa.72.8.

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Efimov, Dmitry. "The Hafnian and a Commutative Analogue of the Grassmann Algebra." Electronic Journal of Linear Algebra 34 (February 21, 2018): 54–60. http://dx.doi.org/10.13001/1081-3810.3467.

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A close relationship between the determinant, the pfaffian, and the Grassmann algebra is well-known. In this paper, a similar relation between the permanent, the hafnian, and a commutative analogue of the Grassmann algebra is described. Using the latter, some new properties of the hafnian are proved.

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Gatto, Letterio, and Taíse Santiago. "Schubert Calculus on a Grassmann Algebra." Canadian Mathematical Bulletin 52, no. 2 (2009): 200–212. http://dx.doi.org/10.4153/cmb-2009-023-x.

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AbstractThe (classical, small quantum, equivariant) cohomology ring of the grassmannian G(k, n) is generated by certain derivations operating on an exterior algebra of a free module of rank n (Schubert calculus on a Grassmann algebra). Our main result gives, in a unified way, a presentation of all such cohomology rings in terms of generators and relations. Using results of Laksov and Thorup, it also provides a presentation of the universal factorization algebra of a monic polynomial of degree n into the product of two monic polynomials, one of degree k.

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Kassenova, T. K., P. Yu Tsyba, and O. V. Razina. "Eight-vertex model over Grassmann algebra." Journal of Physics: Conference Series 1391 (November 2019): 012035. http://dx.doi.org/10.1088/1742-6596/1391/1/012035.

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Ribeiro Tomaz da Silva, Viviane. "ℤ2-Codimensions of the Grassmann Algebra". Communications in Algebra 37, № 9 (2009): 3342–59. http://dx.doi.org/10.1080/00927870802502829.

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Dissertations / Theses on the topic "Grassmann-Algebra"

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Manuel, Alex Sandro Faria 1975. "Identidades polinomiais da álgebra de Grassmann em característica positiva." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307604.

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Orientador: Lucio Centrone<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T01:00:17Z (GMT). No. of bitstreams: 1 Manuel_AlexSandroFaria_M.pdf: 1576341 bytes, checksum: 9b70b637adbe03cbed89830126b23521 (MD5) Previous issue date: 2014<br>Resumo: Esta dissertação foi escrita com a intenção de conter os seus principais pré-requisitos. Assim, inicialmente, recordaremos algumas definições básicas e alguns resultados da álgebra clássica. Então, listaremos alguns resultados clássicos

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Mello, Thiago Castilho de 1984. "Identidades polinomiais em álgebras matriciais sobre a álgebra de Grassmann." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306366.

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Orientador: Plamen Emilov Kochloukov<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-19T21:39:41Z (GMT). No. of bitstreams: 1 Mello_ThiagoCastilhode_D.pdf: 1364753 bytes, checksum: 66955ce4a4c6b84e5c6dcc1a414f3f24 (MD5) Previous issue date: 2012<br>Resumo: Nesta tese estudamos a álgebra genérica de M1;1 em dois geradores sobre um corpo infinito de característica diferente de 2. Descrevemos o centro desta álgebra e provamos que este é a soma direta do corpo com um ideal nilpotente da

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Mastromarino, Claudio. "Analisi di sistemi fermionici mediante variabili di Grassmann." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19143/.

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Il presente elaborato è finalizzato ad esporre come alcuni sistemi fermionici possano essere descritti, anche a livello classico, mediante l’utilizzo di un nuovo sistema di variabili, dette Variabili di Grassmann. Queste variabili godono di proprietà peculiari che le rendono uno strumento efficace per ricavare informazioni e caratteristiche fisiche del sistema in esame. Si introduce la distinzione tra bosoni e fermioni e si dà un breve accenno al Principio di esclusione di Pauli. Successivamente, mediante un breve excursus storico sulla vita di Hermann Günther Grassmann, si chiarisce come e

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Barros, Paulo Barbosa. "Algumas Aplicações de Integrais de Trajetória Grassmannianas na Teoria Quântica Moderna." Universidade de São Paulo, 1998. http://www.teses.usp.br/teses/disponiveis/43/43133/tde-27022014-132628/.

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Este trabalho é dedicado à aplicação de integrais de trajetória de Grassmann para o cálculo de operadores relevantes aos problemas da teoria quântica relativística. Primeiramente uma visão geral detalhada do método é fornecida. Então concentramos nas definições e aplicações das integrais de trajetória sobre as variáveis de Grassmann. Discutimos, em detalhe, um importante papel das integrais de trajetória de Grassmann na representação de propagadores de partículas relativísticas. Derivamos o chamado fatores de spin para tais representações, fazendo as integrações Grasmannianas. Uma contribuição

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Gonçalves, Dimas José. "A-identidades polinomiais em algebras associativas." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306369.

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Orientador: Plamen Emilov Koshlukov<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-12T22:59:30Z (GMT). No. of bitstreams: 1 Goncalves_DimasJose_D.pdf: 561175 bytes, checksum: 463bf9f78a417a27d1bcf83549bc65a9 (MD5) Previous issue date: 2009<br>Resumo: Nesta tese estudamos identidades polinomiais em álgebras associativas. Mais precisamente, estudamos as A-identidades satisfeitas por algumas classes importantes de álgebras. O primeiro resultado principal da tese consiste em uma descriçã

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Fonseca, Marlon Pimenta. "Representações dos grupos simétrico e alternante e aplicações às identidades polinomiais." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/5912.

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Made available in DSpace on 2016-06-02T20:28:31Z (GMT). No. of bitstreams: 1 6450.pdf: 757192 bytes, checksum: 765b66ca6aed0686ecbcd10c145cefac (MD5) Previous issue date: 2014-11-28<br>Financiadora de Estudos e Projetos<br>In this dissertation we ll present a discussion about the Representations of the Symmetric Group Sn and Alternating Group An. We ll study basics results of the Young s Theory about the representations of the Symmetric Group and discover the decomposition of the algebra FSn in simple subalgebras. After, we ll utilize this decomposition to find the decomposition of the algeb

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Allegra, Nicolas. "Propriétés critiques des modèles de dimères, de chaînes de spin et d’interfaces." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0203/document.

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L’étude réalisée dans cette thèse porte sur les phénomènes critiques classiques et quantiques. En effet, les phénomènes critiques et les transitions de phases sont devenus des sujets fondamentaux en physique statistique moderne et en théorie des champs et nous proposons dans cette thèse d’étudier certains modèles qui présentent un comportement critique, à la fois à l’équilibre et hors de l’équilibre. Dans la première partie de la thèse, certaines propriétés du modèle de dimères à deux dimensions sont étudiées. Ce modèle a été largement étudié dans les communautés de physique statistique et de

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Bushman, Nathan. "Hypercomplex Numbers and Early Vector Systems: A History." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1585666516546138.

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Rudolph, Michael. "Untersuchung von Eichfeldtheorien in Termen von lokalen eichinvarianten Größen." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-36498.

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Im Rahmen des Funktionalintegralzugangs zur Quanteneichfeldtheorie wird in der vorliegenden Arbeit eine Quantisierungsprozedur in Termen eichinvarianter Felder vorgeschlagen und am Beispiel zwei- und vierdimensionaler abelscher Modelle (Thirring-Modell und QED) sowie der One-Flavour QCD konkret realisiert. Dazu wird die Algebra der aus der eichabhängigen Feldkonfiguration der zugrunde liegenden Quantenfeldtheorie gebildeten eichinvarianten Grassmann-Algebra-wertigen Differentialformen, welche die Struktur einer Z_2-graduierten Differentialalgebra trägt, näher untersucht. Danach erfolgt die Imp

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Savas, Berkant. "Algorithms in data mining using matrix and tensor methods." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11597.

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In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. The development of mathematical models and efficient algorithms is of key importance. In this thesis we discuss algorithms for the reduced rank regression problem and algorithms for the computation of the best multilinear rank approximation of tensors. The first two papers deal with the reduced rank regression problem,

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Books on the topic "Grassmann-Algebra"

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Understanding geometric algebra: Hamilton, Grassmann, and Clifford for computer vision and graphics. CRC Press, 2015.

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Manivel, Laurent. Fonctions symétriques, polynômes de Schubert et lieux de dégénérescence. Société Mathématique de France, 1998.

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Mann, Peter. Calculus of Variations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0036.

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This chapter presents an introduction to linear algebra. Classical mechanics is best understood in the language of differential geometry, which itself requires a working knowledge of the key concepts in linear algebra. This chapter walks through the required knowledge from this broad discipline and guides the reader towards the goal of the next chapter, differential geometry. Topics discussed include vector spaces, linear maps, basis sets, cobases, inner products, tensors, wedge products and exterior algebra, as well as the axioms of vector space geometry. The chapter concludes with a brief di

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Klein, Felix. Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis. Dover Publications, 2004.

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Klein, Felix. Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis. Cosimo Classics, 2007.

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Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis (Dover Books on Mathematics). Dover Publications, 2004.

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Klein, Felix. Elementary Mathematics from an Advanced Standpoint: Geometry. Dover Publications, 2004.

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Elementary Mathematics from an Advanced Standpoint: Geometry (Dover Books on Mathematics). Dover Publications, 2004.

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Book chapters on the topic "Grassmann-Algebra"

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Federer, Herbert. "Grassmann algebra." In Geometric Measure Theory. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_2.

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Berezin, Felix Alexandrovich. "Grassmann Algebra." In Introduction to Superanalysis. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-017-1963-6_2.

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Xambó-Descamps, Sebastià. "Grassmann Algebra." In SpringerBriefs in Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00404-0_2.

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Wegner, Franz. "Grassmann Algebra." In Supermathematics and its Applications in Statistical Physics. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49170-6_2.

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Howie, John, Steven Duplij, Ali Mostafazadeh, Masaki Yasue, and Vladimir Ivashchuk. "Infinite-Dimensional Grassmann-Banach Algebra." In Concise Encyclopedia of Supersymmetry. Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_264.

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Zeidler, Eberhard. "Algebras and Duality (Tensor Algebra, Grassmann Algebra, Clifford Algebra, Lie Algebra)." In Quantum Field Theory III: Gauge Theory. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22421-8_3.

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White, Neil L. "A Tutorial on Grassmann-Cayley Algebra." In Invariant Methods in Discrete and Computational Geometry. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8402-9_5.

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Jancewicz, Bernard. "The Extended Grassmann Algebra of R3." In Clifford (Geometric) Algebras. Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-4104-1_28.

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Li, Hongbo. "Trifocal Tensors with Grassmann-Cayley Algebra." In Robot Vision. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44690-7_29.

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Doran, Chris, Anthony Lasenby, and Steve Gull. "Grassmann Mechanics, Multivector Derivatives and Geometric Algebra." In Spinors, Twistors, Clifford Algebras and Quantum Deformations. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1719-7_26.

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Conference papers on the topic "Grassmann-Algebra"

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Kodrnja, Iva, Maja Banicek, and Krešimir Fresl. "Grassmann Algebra and Graphic Statics." In Future Trends in Civil Engineering 2019. University of Zagreb Faculty of Civil Engineering, 2019. http://dx.doi.org/10.5592/co/ftce.2019.14.

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Amine, Semaan, Mehdi Tale Masouleh, Ste´phane Caro, Philippe Wenger, and Cle´ment Gosselin. "Singularity Analysis of the 4-RUU Parallel Manipulator Based on Grassmann-Cayley Algebra and Grassmann Geometry." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48226.

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This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Scho¨nflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The study is developed through the singularity analysis of the 4-RUU parallel manipulator. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity, namely, two constraint moments, among its six Plu¨cker lines. The Grassmann-Cayley Algebra is used to obtain geometric singularity conditions. However, due to the presence of lines at infinity, the rank de

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Sheffer, Avshalom, and Offer Shai. "Combinatorial Method for Characterizing Singular Configurations in Parallel Mechanisms." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46755.

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The paper presents a method for finding the different singular configurations of several types of parallel mechanisms/robots using the combinatorial method. The main topics of the combinatorial method being used are: equimomental line/screw, self-stresses, Dual Kennedy theorem and circle, and various types of 2D and 3D Assur Graphs such as: triad, tetrad and double triad. The paper introduces combinatorial characterization of 3/6 SP and compares it to singularity analysis of 3/6 SP using Grassmann Line Geometry and Grassmann-Cayley Algebra. Finally, the proposed method is applied for character

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Lee, Chung-Ching. "Applications of the 4D Geometric Algebra to Dimensional Mobility Criteria of Delassus-Parallelogram and Bennett Paradoxical Linkages." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46667.

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Geometric algebra is also termed Clifford-Grassmann algebra or hypercomplex number. It allows studying space geometric problems in an easy and compact way. Transforming three-dimensional (3D) Euclidean geometric entities to actual elements of four-dimensional (4D) geometric algebra (abbreviated to g4) through a methodical approach of geometric algebra, one can describe motion displacements as even elements of g4. This article relies on the combined rotation and translation in g4 to establish the dimensional constraints of two non-exceptional overconstrained paradoxical linkages. Firstly, funda

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Rasoulzadeh, Arvin, and Mehdi Tale Masouleh. "Singularity configurations analysis of a 4-DOF parallel mechanisms using Grassmann-Cayley Algebra." In 2016 4th International Conference on Robotics and Mechatronics (ICROM). IEEE, 2016. http://dx.doi.org/10.1109/icrom.2016.7886850.

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Amine, Semaan, Daniel Kanaan, Ste´phane Caro, and Philippe Wenger. "Constraint and Singularity Analysis of Lower-Mobility Parallel Manipulators With Parallelogram Joints." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28483.

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This paper presents a general approach to analyze the singularities of lower-mobility parallel manipulators with parallelogram joints. Using screw theory, the concept of twist graph is introduced and the twist graphs of two types of parallelogram joints are established in order to simplify the constraint analysis of the manipulators under study. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plu¨cker vectors of finite and infinite lines in the 3-dimensional projective space are reformulated in the superbracket in order to derive the geometric con

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El-Ghazaly, Gamal, and Stéphane Caro. "Conceptual Design of Lower-Mobility Parallel Manipulators Based on Wrench Graphs." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35494.

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This paper presents a design methodology for lower-mobility parallel manipulators based on classification of wrench systems into four main classes. Wrench systems are represented in a three-dimensional projective space ℙ3 using wrench graphs where it is easy to incorporate geometric constraints to have simple singularity conditions using Grassmann-Cayley algebra (GCA). The main idea of the approach is to design a PM with an overall (constraint and actuation) wrench system that complies with a given wrench graph for which singularity conditions have been predetermined. The main advantage of thi

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