Mathematics – Representation Theory
Scientific paper
2011-09-19
Mathematics
Representation Theory
20 pages
Scientific paper
In this paper we provide more counterexamples to Happel's question and Snashall-Solberg's conjecture which generalize many counterexamples to these conjectures studied in the literature. In particular, we show that a family of $\mathbb{Z}_n\times \mathbb{Z}_n$-Galois covering algebras of quantized exterior algebra $A_q$ in two variables answer negatively to Happel's question, and meanwhile, the one-point coextensions of $\mathbb{Z}_n$ and $\mathbb{Z}_n\times \mathbb{Z}_m$-Galois covering algebras of $A_q$ negate the Snashall-Solberg's conjecture.
Xu Yunge
Zhang Chao
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