Topic
Symmetric algebra
About: Symmetric algebra is a research topic. Over the lifetime, 3738 publications have been published within this topic receiving 83601 citations.
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01 Jun 1969
TL;DR: In this article, Grassmann algebras of a vectorspace have been studied in the context of the calculus of variations, and a glossary of some standard notations has been provided.
Abstract: Introduction Chapter 1 Grassmann algebra 1.1 Tensor products 1.2 Graded algebras 1.3 Teh exterior algebra of a vectorspace 1.4 Alternating forms and duality 1.5 Interior multiplications 1.6 Simple m-vectors 1.8 Mass and comass 1.9 The symmetric algebra of a vectorspace 1.10 Symmetric forms and polynomial functions Chapter 2 General measure theory 2.1 Measures and measurable sets 2.2 Borrel and Suslin sets 2.3 Measurable functions 2.4 Lebesgue integrations 2.5 Linear functionals 2.6 Product measures 2.7 Invariant measures 2.8 Covering theorems 2.9 Derivates 2.10 Caratheodory's construction Chapter 3 Rectifiability 3.1 Differentials and tangents 3.2 Area and coarea of Lipschitzian maps 3.3 Structure theory 3.4 Some properties of highly differentiable functions Chapter 4 Homological integration theory 4.1 Differential forms and currents 4.2 Deformations and compactness 4.3 Slicing 4.4 Homology groups 4.5 Normal currents of dimension n in R(-63) superscript n Chapter 5 Applications to the calculus of variations 5.1 Integrands and minimizing currents 5.2 Regularity of solutions of certain differential equations 5.3 Excess and smoothness 5.4 Further results on area minimizing currents Bibliography Glossary of some standard notations List of basic notations defined in the text Index
6,513 citations
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TL;DR: In this article, the structure and representations of the universal enveloping algebra U(g) were studied for g = g[(N+1) the structure of the algebra Ŭ(g), a q-analogue of the Universal Enveloping Algebra (U(g)).
Abstract: We study for g=g[(N+1) the structure and representations of the algebra Ŭ(g), a q-analogue of the universal enveloping algebra U(g). Applying the result, we construct trigonometric solutions of the Yang-Baxter equation associated with higher representations of g.
1,538 citations
01 Jan 2012
TL;DR: A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.
Abstract: 1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed
1,289 citations