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Ilaria Damiani

Publications and source records attributed to Ilaria Damiani.

5 recordsLinked to original sources
arXiv2020

On the integral form of rank 1 Kac-Moody algebras

In this paper we shall prove that the subalgebra generated over the integers by the divided powers of the Drinfeld generators $x_r^{\pm}$ of the Kac-Moody algebra of type $A_2^{(2)}$ is an integral form (strictly smaller than Mitzman's (see [Mi]) of the enveloping algebra, we shall exhibit a basis generalizing the one provided by Garland in [G] for the untwisted affine Kac-Moody algebras, and we shall determine explicitly the commutation relations. Moreover we prove that both in the untwisted and in the twisted case the positive (respectively negative) imaginary part of the integral form is an algebra of polynomials over the integers.

math.RT↗
arXiv2014

From the Drinfeld realization to the Drinfeld-Jimbo presentation of affine quantum algebras: the injectivity

In this paper the surjective homomorphism from the Drinfeld realization to the Drinfeld and Jimbo presentation of affine quantum algebras is proved to be injective. A consequence of the arguments used in the paper is the triangular decomposition of the Drinfeld realization of affine quantum algebras also in the twisted case. A presentation of the affine Kac-Moody algebras in terms of the "Drinfeld generators" is also provided.

math.QA↗
arXiv2014

Drinfeld Realization of Affine Quantum Algebras: The Relations

In this paper the structure of the Drinfeld realization $\Udr_q$ of affine quantum algebras (both untwisted and twisted) is described in details, and its defining relations are studied and simplified. As an application, a homomorphism $ψ$ from this realization to the Drinfeld and Jimbo presentation $\U_q^{DJ}$ is provided, and proved to be surjective.

math.QA↗