5 citations · 7 across the 12 of their papers we have counts for
13 papers
Gaussian solutions to the Yang--Baxter equation and their twists
Yasmeen S. Baki, Padmini Veerapen
In this paper, we consider two explicit Gaussian solutions to the constant (or parameter-independent) quantum Yang--Baxter equation and produce the corresponding bialgebras using t…
Quantum-symmetric equivalence for superpotential algebras
Hongdi Huang, Van C. Nguyen, Kent B. Vashaw +2
We study superpotential algebras by introducing the notion of quantum-symmetric equivalence defined relatively to two fixed Hopf coactions. This concept relies on the non-vanishing…
Quantum-symmetric equivalence is a graded Morita invariant
Hongdi Huang, Van C. Nguyen, Padmini Veerapen +2
We show that if two -homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalen…
A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry
Pablo S. Ocal, Kenta Ueyama, Padmini Veerapen
We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocy…
Twisting Manin's universal quantum groups and comodule algebras
Hongdi Huang, Van C. Nguyen, Charlotte Ure +3
We introduce the notion of quantum-symmetric equivalence of two connected graded algebras, based on Morita-Takeuchi equivalences of their universal quantum groups, in the sense of…
A cogroupoid associated to preregular forms
Hongdi Huang, Van C. Nguyen, Charlotte Ure +3
We construct a family of cogroupoids associated to preregular forms and recover the Morita-Takeuchi equivalence for Artin-Schelter regular algebras of dimension two, observed by Ra…
Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation
Hongdi Huang, Van C. Nguyen, Charlotte Ure +3
Let be a Hopf algebra that is -graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of to be a Zhang twist of . In particular, we intr…
Reflection Groups and Rigidity of Quadratic Poisson Algebras
Jason Gaddis, Padmini Veerapen, Xingting Wang
In this paper, we study the invariant theory of quadratic Poisson algebras. Let G be a finite group of the graded Poisson automorphisms of a quadratic Poisson algebra A. When the P…
Point modules over regular graded skew Clifford algebras
Michaela Vancliff, Padmini Veerapen
Results of Vancliff, Van Rompay and Willaert in 1998 prove that point modules over a regular graded Clifford algebra (GCA) are determined by (commutative) quadrics of rank at most…
Generalizing the notion of rank to noncommutative quadratic forms
Michaela Vancliff, Padmini Veerapen
In 2010, Cassidy and Vancliff extended the notion of a quadratic form on n generators to the noncommutative setting. In this article, we suggest a notion of rank for such noncommut…
A notion of rank for noncommutative quadratic forms on four generators
Padmini Veerapen, Jessica Cain, Leah Frauendienst
In this paper, we extend previous work, where a notion of rank, called mu-rank, was proposed for noncommutative quadratic forms on two and three generators. In particular, we provi…
Associating Geometry to the Lie Superalgebra and to the Color Lie Algebra
Susan J. Sierra, Špela Špenko, Michaela Vancliff +2
In the 1990s, in work of Le Bruyn and Smith and in work of Le Bruyn and Van den Bergh, it was proved that point modules and line modules over the homogenization of the universal en…
Graded Clifford Algebras and Graded Skew Clifford Algebras and Their Role in the Classification of Artin-Schelter Regular Algebras
Padmini Veerapen
This paper is a survey of work done on -graded Clifford algebras (GCAs) and -graded \textit{skew} Clifford algebras (GSCAs) \cite{VVW, SV, CaV, NVZ, VVe1, V…