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m-Koszul AS-regular algebras and twisted superpotentials

Banff International Research Station for Mathematical Innovation and Discovery

This talk is based on a joint work with S. P. Smith. AS-regular algebras is an important class of algebras to study in noncommutative algebraic geometry. If S is an m-Koszul AS-regular algebra, then it was observed by several people that S is determined by a twisted superpotential. In this talk, we will see that such a twisted superpotential is uniquely determined by S up to non-zero scalar multiples and plays a crucial role in studying S. In particular, we will see in this talk that, using the twisted superpotential w_S associated to S, we can compute (1) the Nakayama automorphism of S, (2) a graded algebra automorphism of S, and (3) the homological determinant of a graded algebra automorphism of S (which is an essential ingredient for invariant theory of an AS-regular algebra). If time permits, we will present some applications to 3-dimensional noetherian Calabi-Yau algebras (which is partially based on a joint work with K. Ueyama).

Mathematics; Associative rings and algebras; Algebraic geometry; Algebraic structures

video/mp4

Author affiliation: Shizuoka University

2017-03-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60947

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/