共查询到10条相似文献,搜索用时 62 毫秒
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基于Furuya构造的一个Cluster-Tilted代数的极小投射双模分解,用组合的方法计算了Cluster-Tilted代数的Hochschild同调空间的维数与基.当基础域的特征为零时,也计算了代数的循环同调群的维数. 相似文献
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《代数通讯》2013,41(11):5653-5671
Abstract In this paper we construct a cylindrical module A ? ? for an ?-comodule algebra A, where the antipode of the Hopf algebra ? is bijective. We show that the cyclic module associated to the diagonal of A ? ? is isomorphic with the cyclic module of the crossed product algebra A ? ?. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a cocylindrical module for Hopf module coalgebras and establish a similar spectral sequence to compute the cyclic cohomology of crossed product coalgebras. 相似文献
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We prove that over a characteristic zero field, in most cases, neither the Hochschild homology algebra of a commutative algebra, nor the free loop space cohomology algebra of a topological space, is finitely generated. 相似文献
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Zuhier Altawallbeh 《代数通讯》2018,46(1):62-68
We construct and study the map from Leibniz homology HL?(𝔥) of an abelian extension 𝔥 of a simple real Lie algebra 𝔤 to the Hochschild homology HH??1(U(𝔥)) of the universal envelopping algebra U(𝔥). To calculate some homology groups, we use the Hochschild-Serre spectral sequences and Pirashvili spectral sequences. The result shows what part of the non-commutative Leibniz theory is detected by classical Hochschild homology, which is of interest today in string theory. 相似文献
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Jerry M. Lodder 《K-Theory》2002,27(4):359-370
For an algebra R over a commutative ring k, a natural homomorphism *: HL*+1(R) HH* (R) from Leibniz to Hochschild homology is constructed that is induced by an antisymmetrization map on the chain level. The map * is surjective when R = gl(A), A an algebra over a characteristic zero field. If f: A B is an algebra homomorophism, the relative groups HL* (gl(f)) are studied, where gl(f): gl(A) gl(B) is the induced map on matrices. Letting HC* denote cyclic homology, if f is surjective with nilpotent kernel, there is a natural surjection HL*+1(gl(f)) HC* (f) in the characteristic zero setting. 相似文献
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For every Ore extension we construct a chain complex giving its Hochschild homology. As an application we compute the Hochschild and cyclic homology of an arbitrary multiparametric affine space and the Hochschild homology of the algebra of differential operators over this space, in the generic case. 相似文献
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Mohammed Abouzaid 《Advances in Mathematics》2011,228(2):894
We prove that the algebra of chains on the based loop space recovers the derived (wrapped) Fukaya category of the cotangent bundle of a closed smooth oriented manifold. The main new idea is the proof that a cotangent fibre generates the Fukaya category using a version of the map from symplectic cohomology to the homology of the free loop space introduced by Cieliebak and Latschev. 相似文献