arXiv subjects

Jiri Hrivnak

Publications and source records attributed to Jiri Hrivnak.

3 recordsLinked to original sources

arXiv2009

Twisted cocycles of Lie algebras and corresponding invariant functions

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint representation - so called $(α,β,γ)$--derivations. Parametric sets of spaces of cocycles allow us to define complex functions which are invariant under Lie isomorphisms. Such complex functions thus represent useful invariants - we show how they classify three and four-dimensional Lie algebras as well as how they apply to some eight-dimensional one-parametric nilpotent continua of Lie algebras. These functions also provide necessary criteria for existence of 1-parametric continuous contraction.

math-ph↗

arXiv2009

On Discretization of Tori of Compact Simple Lie Groups

Three types of numerical data are provided for simple Lie groups of any type and rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series of $C-$ or $S-$functions on the fundamental domain $F$ of the underlying Lie group $G$. Firstly, we consider the number $|F_M|$ of points in $F$ from the lattice $P^{\vee}_M$, which is the refinement of the dual weight lattice $P^{\vee}$ of $G$ by a positive integer $M$. Secondly, we find the lowest set $Λ_M$ of dominant weights, specifying the maximal set of $C-$ and $S-$functions that are pairwise orthogonal on the point set $F_M$. Finally, we describe an efficient algorithm for finding, on the maximal torus of $G$, the number of conjugate points to every point of $F_M$. Discrete $C-$ and $S-$transforms, together with their continuous interpolations, are presented in full generality.

math-ph↗

arXiv2004

Solution of Contraction Equations for the Pauli Grading of sl(3,C)

We consider the Pauli grading of the Lie algebra sl(3,C) and use a concept of graded contractions to construct non-isomorphic Lie algebras of dimension 8, while preserving the Pauli grading. We show how the symmetry group of a grading simplifies the solution of contraction equations. We present the list of all 180 non-equivalent solutions of non-linear contraction system.

hep-th↗