Algebras and Representation Theory
| Autor: | Sibylle Schroll, Lutz Hille, Edward L. Green |
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| Přispěvatelé: | Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Monomial General Mathematics Non-commutative Grobner bases 010102 general mathematics Dimension (graph theory) Algebraic variety 01 natural sciences Global dimension Representation theory of associative algebras 0103 physical sciences FOS: Mathematics 010307 mathematical physics Affine transformation Representation Theory (math.RT) 0101 mathematics Variety (universal algebra) Complex number Associative property Mathematics - Representation Theory Cartan conjecture Mathematics |
| Popis: | 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. 24 pages, v2: added a section on the varieties of algebras of global dimension two |
| Databáze: | OpenAIRE |
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