Algebras and Varieties

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 cases of finite dimensio...

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Bibliographic Details
Published inAlgebras and representation theory Vol. 24; no. 2; pp. 367 - 388
Main Authors Green, Edward L., Hille, Lutz, Schroll, Sibylle
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2021
Springer Nature B.V
Subjects
Algebra
Associative Rings and Algebras
Commutative Rings and Algebras
Complex numbers
Homology
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
16W50
14M05
Global dimension
Representation theory of associative algebras
Cartan conjecture
Non-commutative Gröbner bases
16G20
16S15
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Summary: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 cases 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.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-020-09951-3