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m-Koszul AS-regular algebras and twisted superpotentials Mori, Izuru
Description
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).
Item Metadata
| Title |
m-Koszul AS-regular algebras and twisted superpotentials
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2016-09-16T10:18
|
| Description |
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).
|
| Extent |
59 minutes
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: Shizuoka University
|
| Series | |
| Date Available |
2017-03-17
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0343267
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International