8 citations · 17 across the 4 of their papers we have counts for
6 papers · 2 filters
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…
Generalizations of the Lie superalgebras of supermatrices of complex size and related topics
Pavel Grozman, Dimitry Leites
A class of simple filtered Lie algebras of polynomial growth with increasing filtration is distinguished and presentations of these algebras are explicitely described for the simpl…
Defining relations for classical Lie superalgebras without Cartan matrices
Pavel Grozman, Dimitry Leites, Elena Poletaeva
The analogs of Chevalley generators are offered for simple (and close to them) Z-graded complex Lie algebras and Lie superalgebras of polynomial growth without Cartan matrix. We sh…