219 research outputs found
Remarks on the Schwarzian Derivatives and the Invariant Quantization by means of a Finsler Function
Let be a Finsler manifold. We construct a 1-cocycle on \Diff(M)
with values in the space of differential operators acting on sections of some
bundles, by means of the Finsler function As an operator, it has several
expressions: in terms of the Chern, Berwald, Cartan or Hashiguchi connection,
although its cohomology class does not depend on them. This cocycle is closely
related to the conformal Schwarzian derivatives introduced in our previous
work. The second main result of this paper is to discuss some properties of the
conformally invariant quantization map by means of a Sazaki (type) metric on
the slit bundle induced by Comment: 17 pages; no figures; Latex2e; the exposition has been improved and
new results have been added; to appear in Indag. Mat
Cartan matrices and presentations of the exceptional simple Elduque Lie superalgebra
Recently Alberto Elduque listed all simple and graded modulo 2 finite
dimensional Lie algebras and superalgebras whose odd component is the spinor
representation of the orthogonal Lie algebra equal to the even component, and
discovered one exceptional such Lie superalgebra in characteristic 5. For this
Lie superalgebra all inequivalent Cartan matrices (in other words, inequivalent
systems of simple roots) are listed together with defining relations between
analogs of its Chevalley generators.Comment: 5 pages, 1 figure, LaTeX2
Simple Lie superalgebras and nonintegrable distributions in characteristic p
Recently, Grozman and Leites returned to the original Cartan's description of
Lie algebras to interpret the Melikyan algebras (for p<7) and several other
little-known simple Lie algebras over algebraically closed fields for p=3 as
subalgebras of Lie algebras of vector fields preserving nonintegrable
distributions analogous to (or identical with) those preserved by G(2), O(7),
Sp(4) and Sp(10). The description was performed in terms of
Cartan-Tanaka-Shchepochkina prolongs using Shchepochkina's algorithm and with
the help of SuperLie package. Grozman and Leites also found two new series of
simple Lie algebras.
Here we apply the same method to distributions preserved by one of the two
exceptional simple finite dimensional Lie superalgebras over C; for p=3, we
obtain a series of new simple Lie superalgebras and an exceptional one.Comment: 10 pages; no figure
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