- The Tacit Dimension;
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Nilpotency degree of Lie subalgebras generated by two upper triangular matrices and uniserial representations. In this talk we will recall the basic facts about finite dimensional uniserial representations of Lie algebras and we will give some results about classification. In particular we will present a complete classification of all f.

In this talk we extend the connection between Solomon's descent algebra for the symmetric groups, the Hopf algebra of noncommutative symmetric functions and its descent algebra in the sense of F. Patras to a nonassociative setting by means of universal enveloping algebras of relatively free Sabinin algebras.

## Lie Groups and Lie Algebras I

We also present a nonassociative lifting of the Malvenuto-Reutenauer Hopf algebra of permutations and of the dual of the Hopf algebra of noncommutative quasi-symmetric functions. This lifting is a free nonassociative algebra as well as a cofree graded coassociative coalgebra which also admits an associative inner product that satisfies a Mackey type formula when restricted to its nonassociative Solomon's descent algebra.

In particular, this provides an explicit basis for the Hadamard product of two free monoids in terms of bases of the factors. In this work we show that the category of such elements has a terminal object, which maps via the Fock functor to a Hopf algebra based on permutations, related to the notion of permutation patterns. We obtain a large family of simple modules that have a basis consisting of Gelfand-Tsetlin tableaux and the action of the Lie algebra is given by the Gelfand-Tsetlin formulas.

### mathematics and statistics online

This talk is based in [FRZ19]. Futorny, L.

Ramirez, J. In the talk we present joint work with Diego Lobos. We provide a monomial basis for both algebras. The elements of these bases are parameterized by certain subsets of fully commutative elements. We enumerate these elements according to their affine length. In this talk, we will present the following result and outline its proof:.

## Clifford Algebras and Lie Theory : Eckhard Meinrenken :

This provides an example of semisimple Hopf algebra over a number field not admitting a Hopf order over any cyclotomic ring of integers. The above result appears in [1].

Cuadra and E. Skip to main content. Non-commutative algebra and Lie theory.

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Presentation The general aim of ELAMs is to strenght the interaction and collaborationg among latinoamerican mathematicians giving the opportunity to meet, share their work and discuss issues concerning mathematics in this region. The School will have two main subjects: Non commutative algebra and Lie theory. The School will also include some research conferences.

kinun-mobile.com/wp-content/2020-02-23/viqe-monitoring-app-for.php Administrative and scientific coordinators Paulo Tirao U. Andrea Solotar Univ. Buenos Aires, Argentina, asolotar dm. Andrea Solotar U.