Eugen Rogozinnikov

activity

20212025

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5 papers · 1 filter

math.DG2025

Symplectic groups over Lie subgroups of involutive algebras

Eugen Rogozinnikov

We introduce the symplectic group $Sp_{2} (G, σ)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $σ$ …

math.DG2025

Symmetric spaces for groups over involutive algebras and applications to Higgs bundles

Pengfei Huang, Georgios Kydonakis, Eugen Rogozinnikov +1

We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, σ)$ . In the case when the algebra $(A, σ)$ is Hermitian, or the…

math.DG2024

On double brackets for marked surfaces

Michael Gekhtman, Eugen Rogozinnikov

We propose a construction of a double quasi-Poisson bracket on the group algebra associated to the twisted fundamental group of a marked oriented surface $(S, P)$ with boundary, whe…

math.DG2022

Parametrizing spaces of positive representations

Olivier Guichard, Eugen Rogozinnikov, Anna Wienhard

Using Lusztig's total positivity in split real Lie groups V. Fock and A. Goncharov have introduced spaces of positive (framed) representations. For general semisimple Lie groups a…

math.DG2021

Symplectic groups over noncommutative algebras

Daniele Alessandrini, Arkady Berenstein, Vladimir Retakh +2

We introduce the symplectic group $Sp_{2} (A, σ)$ over a noncommutative algebra $A$ with an anti-involution $σ$ . We realize several classical Lie groups as $Sp_{2}$ ove…