8 citations · 17 across the 4 of their papers we have counts for
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Defining relations for classical Lie algebras of polynomial vector fields
Dimitry Leites, Elena Poletaeva
We explicitly describe the defining relations for simple Lie algebra of vector fields with polynomial coefficients and its subalgebras of divergence free, hamiltonian and contact v…
The analogs of the Riemann tensor for exceptional structures on supermanifolds
Pavel Grozman, Dimitry Leites, Irina Shchepochkina
H. Hertz called any manifold M with a given nonintegrable distribution {\it nonholonomic}. Vershik and Gershkovich stated and R. Montgomery proved that the space of germs of any no…
On unconventional integrations and cross ratio on supermanifolds
Dimitry Leites
The conventional integration theory on supermanifolds had been constructed so as to possess (an analog of) Stokes' formula. In it, the exterior differential d is vital and the inte…
Indecomposable representations of Lie superalgebras
Dimitry Leites
In 1960's I. Gelfand posed a problem: describe indecomposable representations of any simple infinite dimensional Lie algebra of polynomial vector fields. Here, by applying the elem…
The Howe duality and Lie superalgebras
Dimitry Leites, Irina Shchepochkina
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 repr…
Casimir operators for Lie superalgebras
Dimitry Leites, Alexander Sergeev
Casimir operators -- the generators of the center of the enveloping algebra -- are described for simple or close to them ``classical'' finite dimensional Lie superalgebras with non…