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SIMPLE MODULES AND NON-COMMUTATIVE QUADRICS

SØREN JØNDRUP

Matematisk institutt, Københavns Universitet, Universitetsparken 5, DK-2100 København, Denmark

https://doi.org/10.1142/S0219498813500485Cited by:0 (Source: Crossref)

Abstract

In this paper we classify non-commutative quadrics and study their homological properties. In fact we find all non-commutative algebras of degree 2 up to isomorphism and we study these algebras via their homomorphic images onto the polynomial algebra k[x,y] as well as the Ext¹(k(p), k(q))-groups, where k(p) and k(q) are one-dimensional simple modules. Moreover some general results on simple finite-dimensional modules are obtained. Some of these results are applied to the special cases of non-commutative quadrics.

Keywords:

AMSC: 14A22, 14H50, 14R, 16D60, 16G30

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