DG algebras with exterior homology

Hochschild (co)homology of exterior algebras

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

Invariance and Localization for Cyclic Homology of Dg Algebras

We show that two flat differential graded algebras whose derived categories are equivalent by a derived functor have isomorphic cyclic homology. In particular, ‘ordinary’ algebras over a field which are derived equivalent [48] share their cyclic homology, and iterated tilting [19] [3] preserves cyclic homology. This completes results of Rickard’s [48] and Happel’s [18]. It also extends well kno...

On the Hochschild (co)homology of Quantum Exterior Algebras

We compute the Hochschild cohomology and homology of the algebra Λ = k〈x, y〉/(x2, xy + qyx, y2) with coefficients in 1Λψ for every degree preserving k-algebra automorphism ψ : Λ → Λ. As a result we obtain several interesting examples of the homological behavior of Λ as a bimodule.

DG (co)algebras, DG Lie algebras and L∞ algebras

Tensor Algebras, Symmetric Algebras and Exterior Algebras

We begin by defining tensor products of vector spaces over a field and then we investigate some basic properties of these tensors, in particular the existence of bases and duality. After this, we investigate special kinds of tensors, namely, symmetric tensors and skew-symmetric tensors. Tensor products of modules over a commutative ring with identity will be discussed very briefly. They show up...