4-dimensional Artin-Schelter regular quadratic $\tilde{H}_4$-algebras

Kevin De Laet

4-dimensional Artin-Schelter regular quadratic $\tilde{H}_4$-algebras

Rings and Algebras 2019-01-31 v2 Quantum Algebra

Authors: Kevin De Laet

Abstract

In this paper, quadratic algebras on which $\tilde{H}_4$ , the Heisenberg group of order 64, acts as degree-preserving algebra automorphisms are studied. In particular, we show that if $\mathcal{A}$ is a four-dimensional Artin-Schelter regular quadratic $\tilde{H}_4$ -algebra with the degree one part isomorphic to the Schr\"odinger representation of $\tilde{H}_4$ , then $\mathcal{A}$ is (a twist of) a four-dimensional Sklyanin algebra or (a twist of) a quantum Clifford algebra of global dimension 4.

Keywords

quadratic algebra heisenberg group artin-schelter regular sklyanin algebra quantum clifford algebra schrödinger representation

Cite

@article{arxiv.1806.10361,
  title  = {4-dimensional Artin-Schelter regular quadratic $\tilde{H}_4$-algebras},
  author = {Kevin De Laet},
  journal= {arXiv preprint arXiv:1806.10361},
  year   = {2019}
}

Comments

Artin-Schelter regularity should be changed to correct Hilbert series throughout the paper

4-dimensional Artin-Schelter regular quadratic $\tilde{H}_4$-algebras

Abstract

Keywords

Cite

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