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Amir Farahmand Parsa

Publications and source records attributed to Amir Farahmand Parsa.

5 recordsLinked to original sources
arXiv2024

Groups of extended affine Lie type

We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie algebra. Afterwards, we show that the extended affine Weyl group of the ground Lie algebra can be recovered as a quotient group of two subgroups of the group associated to the underlying algebra similar to Kac-Moody groups.

math.QA↗
arXiv2021

Algebraic Semantics for the Logic of Proofs

We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on justification terms and equality predicate on terms. In the end, the completeness theorem and certain generalizations of Stone's representation theorem are obtained for all proposed algebras.

math.LO↗
arXiv2021

Integral structures in extended affine Lie algebras

We construct certain integral structures for the cores of reduced tame extended affine Lie algebras of rank at least 2. One of the main tools to achieve this is a generalization of Chevalley automorphisms in the context of extended affine Lie algebras. As an application, groups of extended affine Lie type associated to the adjoint representation are defined over arbitrary fields.

math.QA↗
arXiv2020

Spin Structures of Kac-Moody Type

We study spin structures on affine Kac-Moody symmetric spaces and obtain sufficient conditions for their existence.\ As a by product of this, we obtain a spin-c representation of certain Kac-Moody quadratic subgroups of type E.

math-ph↗