论文标题
扭曲Manin的通用量子组和综合代数
Twisting Manin's universal quantum groups and comodule algebras
论文作者
论文摘要
我们在Manin的意义上介绍了基于其通用量子群的Morita-Takeuchi等效性，介绍了两个连接的分级代数的量子对称等效性的概念。我们研究量子对称等效类别的同源和代数不变，并证明了数值$ \ mathrm {tor} $ - 规律性，Castelnuovo-Mummord的规律性，Artin-Schelter的规律性，而Frobenius的财产在任何Morita-Takeuchuchiuchiuchi等价下都是不变的。特别是，通过将我们的结果与Raedschelders和van den Bergh的工作相结合，我们证明了固定全局尺寸的Koszul Artin-Schelter常规代数形成单个量子对称等值级别。此外，我们表征了Koszul二元组的2个旋转曲折（作为量子对称对称等效的特殊情况），超电位，超能力代数，nakayama自动形态的扭曲的Frobenius代数和Artin-Schelter常规代数的自动形态。我们还表明，在某些2个循环曲折的情况下保存了有限的Hochschild共同体学环。
We introduce the notion of quantum-symmetric equivalence of two connected graded algebras, based on Morita-Takeuchi equivalences of their universal quantum groups, in the sense of Manin. We study homological and algebraic invariants of quantum-symmetric equivalence classes, and prove that numerical $\mathrm{Tor}$-regularity, Castelnuovo-Mumford regularity, Artin-Schelter regularity, and the Frobenius property are invariant under any Morita-Takeuchi equivalence. In particular, by combining our results with the work of Raedschelders and Van den Bergh, we prove that Koszul Artin-Schelter regular algebras of a fixed global dimension form a single quantum-symmetric equivalence class. Moreover, we characterize 2-cocycle twists (which arise as a special case of quantum-symmetric equivalence) of Koszul duals, of superpotentials, of superpotential algebras, of Nakayama automorphisms of twisted Frobenius algebras, and of Artin-Schelter regular algebras. We also show that finite generation of Hochschild cohomology rings is preserved under certain 2-cocycle twists.
