斜群代数与平凡扩张的表示维数

The Representation Dimensions of Skew Algebra and Its Trivial Extension

设A是域k上的一个有限维自入射代数,G是一个有限群,且G的阶在A中可逆,A*G是斜群代数,T(A)是平凡扩张代数,∧V是外代数.本文证明了A的稳定范畴与A*G的稳定范畴的三角维数相等,得到了∧V*G及T(∧V*G)的表示维数.

Let A be a finite-dimensional selfinjective algebra over k,G be a finite group and the order of G be invertible in ∧,∧ * G be a skew algebra,T(∧) be its trivial extension,∧V be the exterior algebra.In this paper,we show the dimensions of stable module categories of selfinjective algebra and skew algebra over it are equal.In particular we obtain the representation dimensions of ∧V * G and T(∧V * G).