Simple Modules and non-commutative quadrics

TY - JOUR

T1 - Simple Modules and non-commutative quadrics

AU - Jøndrup, Søren

PY - 2013/12

Y1 - 2013/12

N2 - 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.

AB - 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.

U2 - 10.1142/S0219498813500485

DO - 10.1142/S0219498813500485

M3 - Journal article

SN - 0219-4988

VL - 12

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 8

M1 - 1350048

ER -