Non-associative Algebra And Its Applications

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ISBN: 9780824726690 | 0824726693
Cover: Nonspecific Binding
Copyright: 1/13/2006

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With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.

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Mathematical research of Professor Lev Sabinin
Infinite-dimensional representations of the rotation group and magnetic monopoles	p. 1
Generalized Lie nilpotence in integral group rings	p. 9
Lyndon-Shirshov words, Grobner-Shirshov bases, and free Lie algebras	p. 17
Classification of solvable 3-dimensional Lie triple systems	p. 41
Alternating triple systems with simple Lie algebras of derivations	p. 55
The Lie group S[superscript 3] in absolute valued structures	p. 83
The theory of Kikkawa spaces	p. 93
Flexible right-nilalgebras satisfying x(yz)=y(zx)	p. 103
Nijenhuis-Richardson algebra and Frolicher-Nijenhuis Lie module	p. 109
Generalized capable Abelian groups	p. 129
Helicity basis for spin 1/2 and 1	p. 137
A new look at Freudenthal's magic square	p. 149
A survey on approximation of locally compact groups by finite groups, semigroups and quasigroups	p. 167
The transformation algebras of Bernstein graph algebras	p. 183
Central elements of minimal degree in the free alternative algebra	p. 195
Composition, quadratic, and some triple systems	p. 205
An introduction to associator quantization	p. 233
A theorem on Bernstein quadratic integral operators	p. 245
The real prosymmetric spaces	p. 253
Deep matrices and their Frankenstein actions	p. 261
Trace reduction on superspaces	p. 275
Monomorphisms between Cayley-Dickson algebras	p. 281
The notion of lower central series for loops	p. 291
Gravity within the framework of nonassociative geometry	p. 299
Algebras satisfying symmetric triality relations	p. 313
Operads and nonassociative deformations	p. 323
Units of alternative loop rings : a survey	p. 329
Vinberg algebras associated to some nilpotent Lie algebras	p. 347
Algebraic and differential structures in renormalized perturbation quantum field theory	p. 365
Survey on smooth quasigroups development	p. 383
The Lie multiplication in the Lie duals of the Witt algebras	p. 395
Simple decompositions of simple Lie superalgebras	p. 401
The structure and classification of finite division rings	p. 431
Some problems in the theory of rings that are nearly associative	p. 441
Dniester notebook : unsolved problems in the theory of rings and modules	p. 461
Table of Contents provided by Blackwell. All Rights Reserved.

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