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7 papers · 1 filter
Double Poisson brackets on low dimensional algebras
G. I. Sharygin, A. Hernandez Rodriguez
In this paper, we describe double Poisson brackets in the sense of M. Van den Bergh on certain finite-dimensional algebras. In particular we prove that all possible double Poisson…
Split Casimir operator for simple Lie algebras in the cube of -representation and Vogel parameters
A. P. Isaev, S. O. Krivonos, A. A. Provorov
We constructed characteristic identities for the 3-split (polarized) Casimir operators of simple Lie algebras in the adjoint representations and deduced a certain cla…
The split Casimir operator and solutions of the Yang-Baxter equation for the and Lie superalgebras, higher Casimir operators, and the Vogel parameters
A. P. Isaev, A. A. Provorov
We find the characteristic identities for the split Casimir operator in the defining and adjoint representations of the and Lie superalgebras. These identit…
Grassmannian-parameterized solutions to direct-sum polygon and simplex equations
Aristophanes Dimakis, Igor Korepanov
We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structu…
Free fermions on a piecewise linear four-manifold. II: Pachner moves
Igor G. Korepanov
This is the second in a series of papers where we construct an invariant of a four-dimensional piecewise linear manifold with a given middle cohomology class $h\in H^2(M,\mathb…
Free fermions on a piecewise linear four-manifold. I: Exotic chain complex
Igor G. Korepanov
Recently, an algebraic realization of the four-dimensional Pachner move 3--3 was found in terms of Grassmann--Gaussian exponentials, and a remarkable nonlinear parameterization for…