Dialgebra cohomology as a G-algebra

Universal Dialgebra: Unifying Universal Algebra and Coalgebra

The concept of dialgebra provides a platform under which universal algebra and coalgebra are unified in one theory. Other examples of dialgebras include universal multialgebras and partial algebras. In the dialgebraic setting, several relationships between common features of these various theories are clarified and, in many cases, rather similar proofs of closely related results are combined to...

An Embedding of a Dialgebra into an Associative Conformal Algebra

We prove that a dialgebra (coming from K-theory) can be embedded into an associative conformal algebra (coming from conformal field theory). This shows that these notions are related in the same way as ordinary associative algebras related to Lie algebras. The notion of a dialgebra originally appear in K-theory as an analogue of the universal associative envelope for Leibnitz algebras [L1]. On ...

The Cohomology Algebra of a Subalgebra of the Steenrod Algebra

We compute the cohomology algebra of P (1), the subalgebra of the Steenrod algebra generated by P 1 and P p. This completes a partial result given by Arunas Liulevicius in 1962 and provides explicit representatives in the cobar construction for all but one of the algebra generators.

The Hochschild Cohomology of a Poincaré Algebra

In this note, we define the notion of a cactus set, and show that its geometric realization has a natural structure as an algebra over Voronov’s cactus operad, which is equivalent to the framed 2-dimensional little disks operad D2. Using this, we show that for a Poincaré algebra A, its Hochschild cohomology is an algebra over the (chain complexes of) D2.

Tate Cohomology in Commutative Algebra.