Indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level 2 with abelian permutation group
-
Přemysl Jedlička
,
Agata Pilitowska
and
Anna Zamojska-Dzienio
Abstract
We present a construction of all finite indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level at most 2 with abelian permutation group. As a consequence, we obtain a formula for the number of such solutions with a fixed number of elements. We also describe some properties of the automorphism groups in this case; in particular, we show they are regular abelian groups.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level 2 with abelian permutation group
- Extrapolation to product Herz spaces and some applications
- The exact number of orthogonal exponentials on the spatial Sierpinski gasket
- A note on special cubic fourfolds of small discriminants
- Strong multiplicity one for Siegel cusp forms of degree two
- Gross–Prasad periods for reducible representations
- LS-category of moment-angle manifolds and higher order Massey products
- Estimates of heat kernels of non-symmetric Lévy processes
- Global continuity of variational solutions weakening the one-sided bounded slope condition
- Finitary birepresentations of finitary bicategories
- Solvability for nonlocal boundary value problems with generalized 𝑝-Laplacian on an unbounded domain
- Conformal Killing forms on 2-step nilpotent Riemannian Lie groups
- Simply transitive NIL-affine actions of solvable Lie groups
- Mahler measure of 3D Landau–Ginzburg potentials
Articles in the same Issue
- Frontmatter
- Indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level 2 with abelian permutation group
- Extrapolation to product Herz spaces and some applications
- The exact number of orthogonal exponentials on the spatial Sierpinski gasket
- A note on special cubic fourfolds of small discriminants
- Strong multiplicity one for Siegel cusp forms of degree two
- Gross–Prasad periods for reducible representations
- LS-category of moment-angle manifolds and higher order Massey products
- Estimates of heat kernels of non-symmetric Lévy processes
- Global continuity of variational solutions weakening the one-sided bounded slope condition
- Finitary birepresentations of finitary bicategories
- Solvability for nonlocal boundary value problems with generalized 𝑝-Laplacian on an unbounded domain
- Conformal Killing forms on 2-step nilpotent Riemannian Lie groups
- Simply transitive NIL-affine actions of solvable Lie groups
- Mahler measure of 3D Landau–Ginzburg potentials
