230 citations · 1.2k across the 72 of their papers we have counts for
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The Mikheev identity in right Hom-alternative algebras
Donald Yau
It is shown that in every multiplicative right Hom-alternative algebra, a Hom-type generalization of the Mikheev identity holds. It is then inferred that a multiplicative right Hom…
Rota-Baxter Hom-Lie-admissible algebras
Abdenacer Makhlouf, Donald Yau
We study Hom-type analogs of Rota-Baxter and dendriform algebras, called Rota-Baxter -Hom-associative algebras and Hom-dendriform algebras. Several construction results are prov…
Hom-algebras via PROPs
Donald Yau
Hom-algebras over a PROP are defined and studied. Several twisting constructions for Hom-algebras over a large class of PROPs are proved, generalizing many such results in the lite…
A twisted generalization of Novikov-Poisson algebras
Donald Yau
Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products…
Non-commutative Hom-Poisson algebras
Donald Yau
A Hom-type generalization of non-commutative Poisson algebras, called non-commutative Hom-Poisson algebras, are studied. They are closed under twisting by suitable self-maps. Hom-P…
Right Hom-alternative algebras
Donald Yau
It is shown that every multiplicative right Hom-alternative algebra is both Hom-power associative and Hom-Jordan admissible. Multiplicative right Hom-alternative algebras admit Alb…
Hom-power associative algebras
Donald Yau
A generalization of power associative algebra, called Hom-power associative algebra, is studied. The main result says that a multiplicative Hom-algebra is Hom-power associative if…
A Hom-associative analogue of n-ary Hom-Nambu algebras
Donald Yau
It is shown that every n-ary totally Hom-associative algebra with equal twisting maps yields an n-ary Hom-Nambu algebra via an n-ary version of the commutator bracket. The class of…
On n-ary Hom-Nambu and Hom-Maltsev algebras
Donald Yau
Hom-alternative and Hom-Jordan algebras are shown to give rise to Hom-Nambu algebras of arities 2^{k+1} + 1. The class of n-ary Hom-Maltsev algebras is studied. Multiplicative n-ar…
On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
Donald Yau
It is observed that the category of n-ary Hom-Nambu(-Lie) algebras is closed under twisting by self-weak morphisms. Constructions of ternary Hom-Nambu algebras from Hom-associative…
Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
Donald Yau
Hom-Maltsev(-admissible) algebras are defined, and it is shown that Hom-alternative algebras are Hom-Maltsev-admissible. With a new definition of a Hom-Jordan algebra, it is shown…
Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
Donald Yau
We study the Hom-type generalization of infinitesimal bialgebras, called infinitesimal Hom-bialgebras. In particular, we consider infinitesimal Hom-bialgebras arising from quivers,…
Hom-Novikov algebras
Donald Yau
We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov a…
Module Hom-algebras
Donald Yau
We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we cons…
Hom-bialgebras and comodule Hom-algebras
Donald Yau
We study Hom-bialgebras and objects admitting coactions by Hom-bialgebras. In particular, we construct a Hom-bialgebra M representing the functor of 2x2-matrices on Hom-associative…
Hom-algebras and homology
Donald Yau
Classes of -Hom-associative algebras are constructed as deformations of -associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom…
Enveloping algebras of Hom-Lie algebras
Donald Yau
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.
Cohomology and deformation of module-algebras
Donald Yau
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
Gerstenhaber structure and Deligne's conjecture for Loday algebras
Donald Yau
A method for establishing a Gerstenhaber algebra structure on the cohomology of Loday-type algebras is presented. This method is then applied to dendriform dialgebras and three typ…
Deformation theory of dialgebra morphisms
Donald Yau
An algebraic deformation theory of dialgebra morphisms is obtained.
(Co)homology of triassociative algebras
Donald Yau
We study homology and cohomology of triassociative algebras with non-trivial coefficients.