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This updated edition of a classic title studies identical relations
in Lie algebras and also in other classes of algebras, a theory
with over 40 years of development in which new methods and
connections with other areas of mathematics have arisen. New topics
covered include graded identities, identities of algebras with
actions and coactions of various Hopf algebras, and the
representation theory of the symmetric and general linear group.
The volume is introduced with a schedule of the conference sessions
held in May 1998 in Moscow, and a vita of Kurosh (1908-1971), a
forefather of modern algebra affiliated with Moscow State U. The
names of the six sessions offer a sense of the diversity of
participant interests: group theory; theory of rings and modules,
homological algebra, and K-theory; Lie groups and Lie algebras,
invariant theory, and algebraic groups; algebraic geometry,
algebraic number theory, commutative algebra; algebraic systems;
and computer algebra, and algorithmic problems. A sampling of the
32 titles by the international contributors includes: Strictly
stratified algebras; Randomness: algebraic, statistical and
complexity theory aspects; Codimension growth and graded
identities; Birational correspondences of a double cone; Modular
Lie algebras: new trends; and Some notes on universal algebraic
geometry. Lacks an index.
The aim of the Expositions is to present new and important
developments in pure and applied mathematics. Well established in
the community over more than two decades, the series offers a large
library of mathematical works, including several important
classics. The volumes supply thorough and detailed expositions of
the methods and ideas essential to the topics in question. In
addition, they convey their relationships to other parts of
mathematics. The series is addressed to advanced readers interested
in a thorough study of the subject. Editorial Board Lev Birbrair,
Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann,
Columbia University, New York, USA Markus J. Pflaum, University of
Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen,
Germany Katrin Wendland, University of Freiburg, Germany Honorary
Editor Victor P. Maslov, Russian Academy of Sciences, Moscow,
Russia Titles in planning include Yuri A. Bahturin, Identical
Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G.
Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups,
Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems
for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer,
Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical
Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia
Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces
(2021)
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