Algebras and varieties
Representation Theory
2019-11-13 v2
Abstract
In this paper we introduce new affine algebraic varieties whose points correspond to associative algebras. We show that the algebras within a variety share many important homological properties. In particular, any two algebras in the same variety have the same dimension. The case of finite dimensional algebras as well as that of graded algebras arise as subvarieties of the varieties we define. As an application we show that for algebras of global dimension two over the complex numbers, any algebra in the variety continuously deforms to a monomial algebra.
Cite
@article{arxiv.1707.07877,
title = {Algebras and varieties},
author = {Edward L. Green and Lutz Hille and Sibylle Schroll},
journal= {arXiv preprint arXiv:1707.07877},
year = {2019}
}
Comments
24 pages, v2: added a section on the varieties of algebras of global dimension two