Algebras and Varieties
| dc.contributor.author | Green, Edward L. | en |
| dc.contributor.author | Hille, Lutz | en |
| dc.contributor.author | Schroll, Sibylle | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2021-01-06T13:38:20Z | en |
| dc.date.available | 2021-01-06T13:38:20Z | en |
| dc.date.issued | 2020-03 | en |
| dc.description.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 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. | en |
| dc.description.notes | The first and third author were partially supported by an LMS scheme 4 grant. The third author is supported by the EPSRC through the Early Career Fellowship EP/P016294/1. | en |
| dc.description.sponsorship | EPSRCEngineering & Physical Sciences Research Council (EPSRC) [EP/P016294/1]; LMS scheme 4 grant | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | https://doi.org/10.1007/s10468-020-09951-3 | en |
| dc.identifier.eissn | 1572-9079 | en |
| dc.identifier.issn | 1386-923X | en |
| dc.identifier.uri | http://hdl.handle.net/10919/101758 | en |
| dc.language.iso | en | en |
| dc.rights | Creative Commons Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject | Representation theory of associative algebras | en |
| dc.subject | Non-commutative Grobner bases | en |
| dc.subject | Global dimension | en |
| dc.subject | Cartan conjecture | en |
| dc.title | Algebras and Varieties | en |
| dc.title.serial | Algebras and Representation Theory | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |
| dc.type.dcmitype | StillImage | en |
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