Hopf actions on filtered regular algebras

K. Chan; C. Walton; Y. H. Wang; J. J. Zhang

doi:10.1016/j.jalgebra.2013.09.002

Hopf actions on filtered regular algebras

K. Chan
, C. Walton
, Y. H. Wang
, J. J. Zhang

Research output: Contribution to journal › Article › peer-review

Abstract

We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such an algebra with n = 2, for instance. Results on the Gorenstein condition and on the global dimension of the corresponding fixed subrings are also provided.

Original language	English (US)
Pages (from-to)	68-90
Number of pages	23
Journal	Journal of Algebra
Volume	397
DOIs	https://doi.org/10.1016/j.jalgebra.2013.09.002
State	Published - Jan 2014
Externally published	Yes

Keywords

Artin-Schelter regular algebra
Filtered algebra
Fixed subring
Hopf algebra action
Weyl algebras

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/j.jalgebra.2013.09.002

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title = "Hopf actions on filtered regular algebras",

abstract = "We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such an algebra with n = 2, for instance. Results on the Gorenstein condition and on the global dimension of the corresponding fixed subrings are also provided.",

keywords = "Artin-Schelter regular algebra, Filtered algebra, Fixed subring, Hopf algebra action, Weyl algebras",

author = "K. Chan and C. Walton and Wang, \{Y. H.\} and Zhang, \{J. J.\}",

note = "The authors thank the referee for providing many insightful suggestions that improved the exposition of this work. C. Walton and J.J. Zhang were supported by the U.S. National Science Foundation : Grants DMS-1102548 and DMS-0855743 , respectively. Y.H. Wang was supported by the Natural Science Foundation of China : Grants \# 10901098 and \# 11271239 .",

year = "2014",

month = jan,

doi = "10.1016/j.jalgebra.2013.09.002",

language = "English (US)",

volume = "397",

pages = "68--90",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

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T1 - Hopf actions on filtered regular algebras

AU - Chan, K.

AU - Walton, C.

AU - Wang, Y. H.

AU - Zhang, J. J.

N1 - The authors thank the referee for providing many insightful suggestions that improved the exposition of this work. C. Walton and J.J. Zhang were supported by the U.S. National Science Foundation : Grants DMS-1102548 and DMS-0855743 , respectively. Y.H. Wang was supported by the Natural Science Foundation of China : Grants # 10901098 and # 11271239 .

PY - 2014/1

Y1 - 2014/1

N2 - We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such an algebra with n = 2, for instance. Results on the Gorenstein condition and on the global dimension of the corresponding fixed subrings are also provided.

AB - We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such an algebra with n = 2, for instance. Results on the Gorenstein condition and on the global dimension of the corresponding fixed subrings are also provided.

KW - Artin-Schelter regular algebra

KW - Filtered algebra

KW - Fixed subring

KW - Hopf algebra action

KW - Weyl algebras

UR - https://www.scopus.com/pages/publications/84884400067

UR - https://www.scopus.com/pages/publications/84884400067#tab=citedBy

U2 - 10.1016/j.jalgebra.2013.09.002

DO - 10.1016/j.jalgebra.2013.09.002

M3 - Article

AN - SCOPUS:84884400067

SN - 0021-8693

VL - 397

SP - 68

EP - 90

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Hopf actions on filtered regular algebras

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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