Infinite Lie rings

Infinite-dimensional Lie algebras

Infinite Dimensional Lie Groups

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...

Stably Just Infinite Rings

We study just infinite algebras which remain so upon extension of scalars by arbitrary field extensions. Such rings are called stably just infinite. We show that just infinite rings over algebraically closed fields are stably just infinite provided that the ring is either right noetherian (4.2) or countably generated over a large field (6.4). We give examples to show that, over countable fields...

Non-additive Lie centralizer of infinite strictly upper triangular matrices

‎Let $mathcal{F}$ be an field of zero characteristic and $N_{infty‎}(‎mathcal{F})$ be the algebra of infinite strictly upper triangular‎ ‎matrices with entries in $mathcal{F}$‎, ‎and $f:N_{infty}(mathcal{F}‎)rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $‎N_{infty }(mathcal{F})$; that is‎, ‎a map satisfying that $f([X,Y])=[f(X),Y]$‎ ‎for all $X,Yin N_{infty}(mathcal{F})...

Representation Rings of Lie Superalgebras

Given a Lie superalgebra g, we introduce several variants of the representation ring, built as subrings and quotients of the ring RZ2(g) of virtual g-supermodules, up to (even) isomorphisms. In particular, we consider the ideal R+(g) of virtual g-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring SR(g) on which the parity rever...