1) In 1976, looking at simple finite-dimensional complex Lie superalgebras, J.~ Bernstein
and I, and independently M.~ Duflo, observed that certain divergence-free vectorial Lie …

The notion of an odd quasi-connection on a supermanifold, which is loosely an affine
connection that carries non-zero Grassmann parity, is examined. Their torsion and curvature …

Let \mathbfL_k be the holomorphic line bundle of degree k∈\mathbbZ on the projective line.
Here, the tuples (k_1k_2k_3k_4) for which there does not exists homogeneous non-split …

For any Lie supergroup whose underlying Lie group is reductive, we prove an extension of
the Casselman–Wallach globalisation theorem: there is an equivalence between the …

Let V be a complex vector space with a non-degenerate symmetric bilinear form and S an
irreducible module over the Clifford algebra C ℓ (V) determined by this form. A …

We overview classifications of simple infinite-dimensional complex $\mathbb {Z} $-graded
Lie (super) algebras of polynomial growth, and their deformations. A subset of such Lie …

Selected stories about the life of AL Onishchik, and a review of his contribution to the
classification of non-split supermanifolds, in particular, supercurves aka superstrings; his …

Over $\mathbb {C} $, the only non-integrable distributions with infinite-dimensional Lie
algebra of symmetries are the contact one and the Engel one. From the classification of …

We introduce a wide category of superspaces, called locally finitely generated, which
properly includes supermanifolds, but enjoys much stronger permanence properties, as are …

The equations of open 2-dimensional Toda lattice (TL) correspond to Leznov-Saveliev
equations (LSE) interpreted as zero-curvature Yang-Mills equations on the variety of $ O (3) …