53 citations · 216 across the 44 of their papers we have counts for
11 papers · 1 filter
Duality for action bialgebroids
Sophie Chemla, Fabio Gavarini, Niels Kowalzig
We study the effect of linear duality on action bialgebroids (also known as smash product or scalar extension bialgebroids) and, for those bearing a quantisation nature, the effect…
Real forms of complex Lie superalgebras and supergroups
Rita Fioresi, Fabio Gavarini
We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go fr…
Singular Degenerations of Lie Supergroups of Type
Kenji Iohara, Fabio Gavarini
The complex Lie superalgebras of type - also denoted by - are usually considered for "non-singular" values of the parameter ,…
Lie supergroups vs. super Harish-Chandra pairs: a new equivalence
Fabio Gavarini
It is known that there exists a natural functor from Lie supergroups to super Harish-Chandra pairs. A functor going backwards, that associates a Lie supergroup with each super…
Duality features of left Hopf algebroids
Sophie Chemla, Fabio Gavarini, Niels Kowalzig
We explore special features of the pair (U^*, U_*) formed by the right and left dual over a (left) bialgebroid U in case the bialgebroid is, in particular, a left Hopf algebroid. I…
Global splittings and super Harish-Chandra pairs for affine supergroups
Fabio Gavarini
This paper dwells upon two aspects of affine supergroup theory, investigating the links among them. First, I discuss the "splitting" properties of affine supergroups, i.e. special…
Algebraic supergroups of Cartan type
Fabio Gavarini
I present a construction of connected affine algebraic supergroups G_V associated with simple Lie superalgebras g of Cartan type and with g-modules V. Conversely, I prove that ever…
Algebraic supergroups with Lie superalgebras of classical type
Rita Fioresi, Fabio Gavarini
We show that every connected affine algebraic supergroup defined over a field k, with diagonalizable maximal torus and whose tangent Lie superalgebra is a k-form of a complex simpl…
On the construction of Chevalley Supergroups
R. Fioresi, F. Gavarini
We give a description of the construction of Chevalley supergroups, providing some explanatory examples. We avoid the discussion of the , and cases, for which…
Chevalley Supergroups of type D(2,1;a)
Fabio Gavarini
I present a construction "a` la Chevalley" of affine supergroups associated with simple Lie superalgebras of (classical) type D(2,1;a), for any possible value of the parameter a -…
Chevalley Supergroups
R. Fioresi, F. Gavarini
In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associa…