Rational Constructions of Modules for Simple Lie Algebras PDF Download
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Author: George B. Seligman
Publisher: American Mathematical Soc.
ISBN: 0821850083
Category : Mathematics
Languages : en
Pages : 203
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Book Description
Suitable for researchers in Lie theory and in the theory of linear algebra, associative or otherwise, and to graduate students who have had some background in one or more of these areas.
Author: George B. Seligman
Publisher: American Mathematical Soc.
ISBN: 0821850083
Category : Mathematics
Languages : en
Pages : 203
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Book Description
Suitable for researchers in Lie theory and in the theory of linear algebra, associative or otherwise, and to graduate students who have had some background in one or more of these areas.
Author: George B. Seligman
Publisher:
ISBN:
Category :
Languages : en
Pages : 185
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Book Description
Author: George B. Seligman
Publisher: Springer
ISBN: 3540388648
Category : Mathematics
Languages : en
Pages : 203
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Book Description
This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.
Author: James Lepowsky
Publisher: American Mathematical Soc.
ISBN: 0821850482
Category : Mathematics
Languages : en
Pages : 96
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Book Description
The affine Kac-Moody algebra $A_1 DEGREES{(1)}$ has served as a source of ideas in the representation theory of infinite-dimensional affine Lie algebras. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1 DEGREES{(1)}$-modules in the homogeneou
Author: David Mitzman
Publisher: American Mathematical Soc.
ISBN: 0821850431
Category : Mathematics
Languages : en
Pages : 170
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Book Description
A revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.
Author: Bruce Normansell Allison
Publisher: American Mathematical Soc.
ISBN: 0821828118
Category : Mathematics
Languages : en
Pages : 175
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Book Description
Introduction The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra, $r\ge 3$ (excluding type $\mathrm{D}_3)$ Models for $\mathrm{BC}_r$-graded Lie algebras, $r\ge 3$ (excluding type $\mathrm{D}_3)$ The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $\mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.
Author: Georgia Benkart
Publisher: American Mathematical Soc.
ISBN: 0821851195
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Author: Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro
Publisher: American Mathematical Soc.
ISBN: 0821850199
Category : Mathematics
Languages : en
Pages : 84
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Book Description
These are lecture notes of a course given at Tel-Aviv University. The aim of these notes is to present the theory of representations of GL(2, K) where K is a finite field. However, the presentation of the material has in mind the theory of infinite dimensional representations of GL(2, K) for local fields K.
Author: Shimshon A. Amitsur
Publisher: American Mathematical Soc.
ISBN: 082185013X
Category : Mathematics
Languages : en
Pages : 420
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Book Description
Author: Martin Golubitsky
Publisher: American Mathematical Soc.
ISBN: 0821850601
Category : Mathematics
Languages : en
Pages : 408
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Book Description
This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature. The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.
