arXiv subjects

Maria Golenishcheva-Kutuzova

Publications and source records attributed to Maria Golenishcheva-Kutuzova.

2 recordsLinked to original sources

arXiv2005

Higher-Dimensional generalizations of Affine Kac-Moody and Virasoro Lie Algebras

We discuss the higher dimensional generalizations of the Virasoro and Affine Kac-Moody Lie algebras. We present an explicit construction for a central extensions of the Lie Algebra $Map (X, \g)$ where $\g$ is a finite-dimensional Lie algebra and $X$ is a complex manifold that can be described as a "right" higher-dimensional generalization of $C^*$ from the point of view of a corresponding group action. The constructed algebras have most of the good properties of finite dimensional semi-simple Lie algebras and are a new class of generalized Kac-Moody algebras. These algebras have description in terms of higher dimensional local fields.

math.QA↗

arXiv1997

$Γ$-Conformal Algebras

$Γ$-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their representations with an action of the group $Γ$. To every $Γ$-conformal algebra and a character of $Γ$ we associate a Lie algebra generated by fields with the OPE with simple poles. Examples include twisted affine Kac-Moody algebras, the sin algebra (which is a ``$Γ$-conformal'' analodue of the general linear algebra) and its analogues, the algebra of pseudodifferential operators on the circle, etc.

q-alg↗