6 papers
Cohomology and extensions of Novikov algebras of truncated polynomials
Hassan Alhussein
Let $\kk$ be a \emph{field of characteristic , not assumed algebraically closed}, and let $V=\kk[x]/(x^p)$ be the Novikov algebra with product . For $λ\in\kk$, l…
On the Cohomology of Cyclic Associative Algebras
Hassan Alhussein
We introduce a cohomology theory for cyclic associative algebras, a subclass of shift associative algebras defined by the identity . This cohomology, denoted…
Rota-Baxter Operators on Vertex Algebras in Integrated -Bracket Formalism and Their Associated 2-Cocycles
Hassan Alhussein
We study Rota--Baxter operators on vertex algebras using the integrated -bracket formalism. A Rota--Baxter operator produces a deformed vertex algebra structure, and the differe…
A New Approach to Defining Cochain Complexes for Tri-dendriform algebra
Hassan Alhussein
Our constructions provide a systematic way to study cohomology tri-dendriform algebra via classical cohomology, simplifying computations and enabling the use of established techniq…
A New Approach to Defining Cochain Complexes for dual Leibniz algebra
Hassan Alhussein
We construct a cochain map embedding the cohomology complex of any dual Leibniz algebra into the Lie algebra cochain complex of , where i…
A New Approach to Defining Cochain Complexes for Dendriform and Pre-Lie Algebras
H. Alhussein
Our constructions provide a systematic way to study cohomology pre-algebraic structures via classical cohomology, simplifying computations and enabling the use of established techn…