Sara Madariaga

Hopf algebras with triality

In this joint work with G. Benkart and J.M. Perez-Izquierdo, we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows a new construction of the universal enveloping algebras of Malcev algebras. Our work relays on the approach of Grishkov and Zavarnitsine to groups with triality.

STRUCTURE THEORY FOR THE GROUP ALGEBRA OF THE SYMMETRIC GROUP, WITH APPLICATIONS TO POLYNOMIAL IDENTITIES FOR THE OCTONIONS

In part 1, we review the structure theory of

Polynomial Identities for Tangent Algebras of Monoassociative Loops

\mathbb{F} S_n

Splitting of operations for alternative and Malcev structures

, the group algebra of the symmetric group

Permutation of elements in double semigroups

S_n

Gröbner-Shirshov bases for the non-symmetric operads of dendriform algebras and quadri-algebras

over a field of characteristic 0. We define the images

Dendriform Analogues of Lie and Jordan Triple Systems

\psi(E^\lambda_{ij})

Non-Existence of Coassociative Quantized Universal Enveloping Algebras of the Traceless Octonions

of the matrix units

Commutative n-Ary Leibniz Algebras

E^\lambda_{ij}

Linear representations of formal loops

(