منابع مشابه
Hochschild homology of preprojective algebras over the integers
We determine the Z-module structure and explicit bases for the preprojective algebra Π and all of its Hochschild (co)homology, for any non-Dynkin quiver. This answers (and generalizes) a conjecture of Hesselholt and Rains, producing new p-torsion elements in degrees 2p, l ≥ 1. We relate these elements by p-th power maps and interpret them in terms of the kernel of Verschiebung maps from noncomm...
متن کاملOn the cyclic Homology of multiplier Hopf algebras
In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a para...
متن کاملSymmetric Homology of Algebras
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed simplicial groups and the homological algebra of module-valued functors. The symmetric homology of group algebras is related to stable homotopy theory. Two sp...
متن کاملHochschild homology of structured algebras
We give a general method for constructing explicit and natural operations on the Hochschild complex of algebras over any PROP with A∞–multiplication—we think of such algebras as A∞–algebras “with extra structure”. As applications, we obtain an integral version of the Costello-Kontsevich-Soibelman moduli space action on the Hochschild complex of open TCFTs, the Tradler-Zeinalian action of Sulliv...
متن کاملSymmetric Homology of Algebras: Foundations
Symmetric homology of a unital algebra A over a commutative ground ring k is defined using derived functors and the symmetric bar construction of Fiedorowicz. If A = k[G] is a group ring, then HS∗(k[G]) is related to stable homotopy theory. Two chain complexes that compute HS∗(A) are constructed, both making use of a symmetric monoidal category ∆S+ containing ∆S. Two spectral sequences are foun...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01910-7