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Algebras defined by Lyndon words and Artin-Schelter regularity

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Tatiana Gateva-Ivanova
American University in Bulgaria/MPIM
Tue, 2019-05-14 14:00 - 15:00
MPIM Lecture Hall

The classification of Artin-Schelter regular algebras and finding new classes of regular algebras are fundamental problems
in noncommutative algebraic geometry.
 In this talk we consider classes C(X, W) of associative graded algebras A over a
K, generated by a finite set X and with a fixed obstructions set W, where W is a finite antichain of Lyndon words
X. The main question is: when such a class contains an AS regular algebra? Given the global dimension d of A, we
that the order of W satisfies
the inequality d-1 |W|d(d-1)/2. We prove that W is unique, and  C(X, W) contains regular
algebras,  whenever
|W| attains the lower, or the upper bounds.  If the order of W is d(d-1)/2,  C(X, W) contains numerous
non-isomorphic PBW regular algebras, each of which defines a set-theoretic solution of the Yang-Baxter equation.


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