Grobner-shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra
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A01=Kyriakos Kalorkoti
A01=Leonid Bokut
A01=Pavel Kolesnikov
A01=Viktor E Lopatkin
A01=Yuqun Chen
Author_Kyriakos Kalorkoti
Author_Leonid Bokut
Author_Pavel Kolesnikov
Author_Viktor E Lopatkin
Author_Yuqun Chen
Category=PBF
Category=PBMW
Category=PBV
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eq_isMigrated=2
eq_nobargain
GrAfA?bnerAcAEURA"Shirshov Bases
Grobner-Shirshov Bases
Gröbner–Shirshov Bases
Product details
- ISBN 9789814619486
- Publication Date: 29 Jul 2020
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac-Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincaré-Birkhoff-Witt theorem for universal enveloping algebras and Artin-Markov normal form theorem for braid groups in Burau generators.What is now called Gröbner-Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921-1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gröbner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner-Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota-Baxter algebra, operads). This is a general and powerful method in algebra.
