8 citations · 17 across the 4 of their papers we have counts for
14 papers
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…
Lie superalgebra structures in cohomology spaces of Lie algebras with coefficients in the adjoint representation
Alexei Lebedev, Dimitry Leites, Ilya Shereshevskii
The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains a…
On Einstein equations on manifolds and supermanifolds
D. Leites, E. Poletaeva, V. Serganova
The Einstein equations (EE) are certain conditions on the Riemann tensor on the real Minkowski space M. In the twistor picture, after complexification and compactification M become…
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…
Defining relations for the exceptional Lie superalgebras of vector fields pertaining to The Standard Model
Pavel Grozman, Dimitry Leites, Irina Shchepochkina
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 Sta…