设Λ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Λ中可逆, Λ*G是斜群代数, T(Λ)是平凡扩张代数, ΛV是外代数.本文证明了Λ的稳定范畴与Λ*G的稳定范畴的三角维数相等, 得到了ΛV * G及T(ΛV* G)的表示维数.
Abstract
Let Λ be a finite-dimensional selfinjective algebra over k, G be a finite group and the order of G be invertible in Λ, Λ * G be a skew algebra, T(Λ) 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).
关键词
稳定范畴 /
斜群代数 /
表示维数
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Key words
stable category /
skew algebra /
representation dimension
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参考文献
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