230 citations · 1.2k across the 72 of their papers we have counts for
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Hom-quantum groups III: Representations and module Hom-algebras
Donald Yau
We study Hom-quantum groups, their representations, and module Hom-algebras. Two Twisting Principles for Hom-type algebras are formulated, and construction results are proved follo…
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…
Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
Donald Yau
A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided H…
Hom-quantum groups I: quasi-triangular Hom-bialgebras
Donald Yau
We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-tria…
On homotopy invariance for algebras over colored PROPs
Mark W. Johnson, Donald Yau
Over a monoidal model category, under some mild assumptions, we equip the categories of colored PROPs and their algebras with projective model category structures. A Boardman-Vogt…
The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
Donald Yau
Motivated by recent work on Hom-Lie algebras and the Hom-Yang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation (CYBE), called the classi…
The Hom-Yang-Baxter equation and Hom-Lie algebras
Donald Yau
Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by the author in an earlier…
Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras
Donald Yau
We study a twisted version of the Yang-Baxter Equation, called the Hom-Yang-Baxter Equation (HYBE), which is motivated by Hom-Lie algebras. Three classes of solutions of the HYBE a…
The L_\infty-deformation complex of diagrams of algebras
Yael Frégier, Martin Markl, Donald Yau
The deformation complex of an algebra over a colored PROP P is defined in terms of a minimal (or, more generally, cofibrant) model of P. It is shown that it carries the structure o…