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Irina Shchepochkina

Publications and source records attributed to Irina Shchepochkina.

26 records · Page 2Linked to original sources
arXiv2005

How to realize Lie algebras by vector fields

An algorithm for embedding finite dimensional Lie algebras into Lie algebras of vector fields (and Lie superalgebras into Lie superalgebras of vector fields) is offered in a way applicable over ground fields of any characteristic. The algorithm is illustrated by reproducing Cartan's interpretations of the Lie algebra of G(2) as the Lie algebra that preserves certain non-integrable distributions. Similar algorithm and interpretation are applicable to other exceptional simple Lie algebras, as well as to all non-exceptional simple ones and many non-simple ones, and to many Lie superalgebras.

math.RT↗
arXiv2002

Invariant operators on supermanifolds and Standard Models

Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was earlier obtained in 2 of the 15 cases by Kochetkov and in one more instance by Kac and Rudakov. Broadhurst and Kac conjectured that some of these structures pertain to the Standard Models of elementary particles and the Grand Unified Theories. So, GUT, if any exists, will be formulated in terms of operators we found, or their r-nary analogs to be found. Calculations are performed with the aid of Grozman's Mathematica-based SuperLie package. When degeneracy conditions are violated (absence of singular vectors) the corresponding module of tensor fields is irreducible. We consider generalized tensors corresponding to fibers of countable infinite dimension, not only finite dimensional ones. We also verified some of the earlier findings.

math.RT↗
arXiv2002

Defining relations for the exceptional Lie superalgebras of vector fields pertaining to The Standard Model

We list defining relations for the four of the five exceptional simple Lie superalgebras some of which, as David Broadhurst conjectured and Kac demonstrated, may pertain to The Standard Model or Grand unified theories of elementary particles. For the fifth superalgebra the result is not final: there might be infinitely many relations. Contrariwise, for the same Lie superalgebra with Laurent polynomials as coefficients there are only finitely many relations.

math-ph↗
arXiv2002

The Howe duality and Lie superalgebras

Howe's duality is considered from a unifying point of view based on Lie superalgebras. New examples are offered. In particular, we construct several simplest spinor-oscillator representations and compute their highest weights for the 'stringy' Lie superalgebras (i.e., Lie superalgebras of complex vector fields (or their nontrivial central extensions) on the supercircle $S^{1|n}$ and its two-sheeted cover associated with the Möbius bundle).

math.RT↗
arXiv1997

Explicit bracket in the exceptional simple Lie superalgebra cvect(0|3)_*

This note is devoted to a more detailed description of one of the five simple exceptional Lie superalgebras of vector fields, cvect(0|3)_*, a subalgebra of vect(4|3). We derive differential equations for its elements, and solve these equations. Hence we get an exact form for the elements of cvect(0|3)_*. Moreover we realize cvect(0|3)_* by "glued" pairs of generating functions on a (3|3)-dimensional periplectic (odd symplectic) supermanifold and describe the bracket explicitly.

math-ph↗
arXiv1997

Lie superalgebras of string theories

We define and describe simple complex Lie superalgbras of vector fields on "supercircles" - simple stringy superalgebras. There are four series of such algebras and four exceptional stringy superalgebras. The 13 of the simple stringy Lie superalgebras are distinguished: only they have nontrivial central extensions; since two of the distinguish algebras have 3 nontrivial central extensions each, there are exactly 16 superizations of the Liouville action, Schroedinger equation, KdV hierarchy, etc. We also present the three nontrivial cocycles on the N=4 extended Neveu-Schwarz and Ramond superalgebras in terms of primary fields and describe the "classical" stringy superalgebras close to the simple ones. One of these stringy superalgebras is a Kac-Moody superalgebra G(A) with a nonsymmetrizable Cartan matrix A. Unlike the Kac-Moody superalgebras of polynomial growth with symmetrizable Cartan matrix, it can not be interpreted as a central extension of a twisted loop algebra.The stringy superalgebras are often referred to as superconformal ones. We discuss how superconformal stringy superalgebras really are.

hep-th↗
arXiv1997

The five exceptional simple Lie superalgebras of vector fields

The five simple exceptional complex Lie superalgbras of vector fields are described. One of them is new; the other four are explicitely described for the first time. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation. The description of several of the exceptional Lie superalgebras is associated with the Lie superalgebra AS - the nontrivial central extension of the supertraceless subalgebra SPE(4) of the periplectic Lie superalgebra PE(4) that preserves the nondegenerate odd bilinear form on the (4|4)-dimensional superspace. (A nontrivial central extension of SPE(n) only exists for n=4.)

hep-th↗