Nicoletta Cantarini

Spherical orbits and quantized enveloping algebras

Let lbe an odd integerl>1 and let ϵ be a primitive lth -root of unity. In this paper we prove that every Uϵ(sl(n))-irreducible module parametrized by a spherical, unipotent conjugacy class О of SL(n) has dimension divisible by l ½dimОresuit was conjectured by De Concini, Kac and Procesi in [DC-K-P 1].

AUTOMORPHISMS AND FORMS OF SIMPLE INFINITE-DIMENSIONAL LINEARLY COMPACT LIE SUPERALGEBRAS

We describe the group of continous automorphisms of all simple infinite-dimensional linearly compact Lie superalgebras and use it in order to classify 𝔽-forms of these superalgebras over any field 𝔽 of characteristic zero.

Algebraic vs physical N = 6 3-algebras

In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.

Classification of linearly compact simple Nambu-Poisson algebras

We introduce the notion of a universal odd generalized Poisson superalgebra associated with an associative algebra A, by generalizing a construction made in the work of De Sole and Kac [Jpn. J. Math. 8, 1–145 (2013)]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n-Nambu-Poisson algebras over an algebraically closed field of characteristic zero.