Journal article
Hopf actions of some quantum groups on path algebras
Journal of algebra, Vol.587, pp.85-117
12/01/2021
DOI: 10.1016/j.jalgebra.2021.08.002
Abstract
Our first collection of results parametrize (filtered) actions of a quantum Borel U-q(b) subset of U-q(sl(2)) on the path algebra of an arbitrary (finite) quiver. When qis a root of unity, we give necessary and sufficient conditions for these actions to factor through corresponding finite-dimensional quotients, generalized Taft algebras T(r, n) and small quantum groups u(q)(sl(2)).
In the second part of the paper, we shift to the language of tensor categories. Here we consider a quiver path algebra equipped with an action of a Hopf algebra H to be a tensor algebra in the tensor category of representations H. Such a tensor algebra is generated by an algebra and bimodule in this tensor category. Our second collection of results describe the corresponding bimodule categories via an equivalence with categories of representations of certain explicitly described quivers with relations. (C) 2021 Elsevier Inc. All rights reserved.
Details
- Title: Subtitle
- Hopf actions of some quantum groups on path algebras
- Creators
- Ryan Kinser - University of IowaAmrei Oswald - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of algebra, Vol.587, pp.85-117
- DOI
- 10.1016/j.jalgebra.2021.08.002
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Number of pages
- 33
- Grant note
- 636534 / Simons Foundation
- Language
- English
- Date published
- 12/01/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984240868202771
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