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Unitary representations of the Virasoro algebra and a conjecture of Kac

Vyjayanthi Chari, Andrew Pressley (1988)

Compositio Mathematica

Unitary structure in representations of infinite-dimensional groups and a convexity theorem.

V.G. Kac, D.H. Peterson (1984)

Inventiones mathematicae

Universal Bethe ansatz and scalar products of Bethe vectors.

Belliard, Samuel, Pakuliak, Stanislav, Ragoucy, Eric (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Universal central extension of direct limits of Hom-Lie algebras

Valiollah Khalili (2019)

Czechoslovak Mathematical Journal

We prove that the universal central extension of a direct limit of perfect Hom-Lie algebras $(ℒ_{i}, α_{ℒ_{i}})$ is (isomorphic to) the direct limit of universal central extensions of $(ℒ_{i}, α_{ℒ_{i}})$ . As an application we provide the universal central extensions of some multiplicative Hom-Lie algebras. More precisely, we consider a family of multiplicative Hom-Lie algebras ${({sl}_{k} (å), α_{k})}_{k \in I}$ and describe the universal central extension of its direct limit.

Universal enveloping algebras of Leibniz algebras and (co)homology.

Jean-Louis Loday, Teimuraz Priashvili (1993)

Mathematische Annalen

Universal lifting theorem and quasi-Poisson groupoids

David Inglesias-Ponte, Camille Laurent-Gengoux, Ping Xu (2012)

Journal of the European Mathematical Society

We prove the universal lifting theorem: for an $α$ -simply connected and $α$ -connected Lie groupoid $Γ$ with Lie algebroid $A$ , the graded Lie algebra of multi-differentials on $A$ is isomorphic to that of multiplicative multi-vector fields on $Γ$ . As a consequence, we obtain the integration theorem for a quasi-Lie bialgebroid, which generalizes various integration theorems in the literature in special cases. The second goal of the paper is the study of basic properties of quasi-Poisson groupoids. In particular,...