73 citations · 164 across the 18 of their papers we have counts for
6 papers · 1 filter
Involutive Yang-Baxter: cabling, decomposability, Dehornoy class
V. Lebed, S. Ramírez, L. Vendramin
We develop new machinery for producing decomposability tests for involutive solutions to the Yang-Baxter equation. It is based on the seminal decomposability theorem of Rump, and o…
Reflection equation as a tool for studying solutions to the Yang-Baxter equation
V. Lebed, L. Vendramin
Given a right-non-degenerate set-theoretic solution to the Yang-Baxter equation, we construct a whole family of YBE solutions on indexed by its reflections $k…
On structure groups of set-theoretic solutions to the Yang-Baxter equation
V. Lebed, L. Vendramin
This paper explores the structure groups of finite non-degenerate set-theoretic solutions to the Yang-Baxter equation. Namely, we construct a finite quotient $\…
Representations of crossed modules and other generalized Yetter-Drinfel'd modules
Victoria Lebed, Friedrich Wagemann
The Yang-Baxter equation plays a fundamental role in various areas of mathematics. Its solutions, called braidings, are built, among others, from Yetter-Drinfel'd modules over a Ho…
Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
V. Lebed, L. Vendramin
This paper deals with left non-degenerate set-theoretic solutions to the Yang-Baxter equation (=LND solutions), a vast class of algebraic structures encompassing groups, racks, and…
Braided Systems: a Unified Treatment of Algebraic Structures with Several Operations
Victoria Lebed
Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop…