共查询到17条相似文献,搜索用时 62 毫秒
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本文利用组合的方法, 详细地计算了一类量子Koszul 代数Λq (q ∈ k \{0}) 的各阶Hochschild 上同调空间的维数, 清晰地刻划了代数Λq 的Hochschild 上同调的cup 积, 确定了代数Λq 的Hochschild上同调环HH*(Λq) 模去幂零元生成的理想N 的结构, 证明了当q 为单位根时, HH*(Λq)/N 作为代数不是有限生成的, 从而为Snashall-Solberg 猜想(即HH*(Λ)/N 作为代数是有限生成的) 提供了更多反例. 相似文献
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考虑一类量子Koszul代数的
${\mathbb{Z}}_{2}$-Galois覆盖$\Lambda_{\q}$, 并计算
这类代数的各阶Hochschild上同调群的维数,
进而利用道路的语言, 刻画了 Hochschild上同调环的cup积. 作为应用,
给出了这类代数的Hochschild上同调环模掉幂零理想的
代数结构. 相似文献
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本文给出了拟entwining结构的概念,研究了拟entwining结构的Hochschild上同调,得到了关于拟entwining结构的Hochschild上同调的等价定理.特别地,对于有限维代数和余代数的拟entwining结构,给出了余代数结构的Hochschild上同调与对偶代数结构的Hochschild上同调之间的同构定理. 相似文献
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本文基于四项正合序列,利用组合的方法给出了具有正规基的特殊双列代数的一阶和二阶Hochschild上同调群的维数公式. 相似文献
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令$A$是代数闭域$k$上的一个有限维结合代数, $\mod A$是有限维左$A$-模范畴,$X_1,X_2,\ldots,X_n$是$\mod A$中的完全例外序列,再令$E$是$X_1,X_2,\ldots,X_n$的自同态代数,我们在本文内,研究了$E$的总体维数,计算了$E$的Hochschild上同调群和同调群. 相似文献
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本文研究一类量子代数$\Lambda^n_q$的Hochschild上同调.量子代数$\Lambda^n_q$的极小投射双模分解被构造, $\Lambda^n_q$的各阶Hochschild上同调群的维数被清晰的给出.此外,对一些特殊的情况, $\Lambda^n_q$的上同调环也被清晰的刻画. 相似文献
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Let Λ be a Fibonacci algebra over a field k. The multiplication of Hochschild cohomology ring of Λ induced by the Yoneda product is described explicitly. As a consequence,
the multiplicative structure of Hochschild cohomology ring of Λ is proved to be trivial. 相似文献
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Hochschild cohomology of special biserial algebras 总被引:1,自引:0,他引:1
Yun-ge Xu 《中国科学A辑(英文版)》2007,50(8):1117-1128
Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics. 相似文献
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Yun-ge XU Yang HAN & Wen-feng JIANG Faculty of Mathematics & Computer Science Hubei University Wuhan China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(5):727-736
For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. 相似文献
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Fei Xu 《Advances in Mathematics》2008,219(6):1872-1893
Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH∗(kC)→H∗(|C|,k) and prove it is split surjective, using the factorization category of Quillen [D. Quillen, Higher algebraic K-theory I, in: Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85-147] and certain techniques from functor cohomology theory. This generalizes the well-known theorems for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, disproving a conjecture of Snashall and Solberg [N. Snashall, Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (3) (2004) 705-732]. 相似文献
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Anne V. Shepler Sarah Witherspoon 《Transactions of the American Mathematical Society》2008,360(8):3975-4005
We develop and collect techniques for determining Hochschild cohomology of skew group algebras and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of and, in particular, about graded Hecke algebras. We expand the definition of a graded Hecke algebra to allow a nonfaithful action of on , and we show that there exist nontrivial graded Hecke algebras for , in contrast to the case of the natural reflection representation. We prove that one of these graded Hecke algebras is equivalent to an algebra that has appeared before in a different form.
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Hochschild cohomology of truncated basic cycle 总被引:9,自引:0,他引:9
Pu Zhang 《中国科学A辑(英文版)》1997,40(12):1272-1278
Dimensions of the Hochschild cohomology groups of a truncated algebra of a basic cycle are explicitly given.
Project supported by the State Education Commission of China, the Chinese Academy of Sciences and the National Natural Science
Foundation of China. 相似文献