Universal central extensions of elliptic affine Lie algebras

DOI10.1063/1.530700zbMath0839.17017OpenAlexW2100591101MaRDI QIDQ4837155

Murray R. Bremner

Publication date: 4 July 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530700

zbMATH Keywords

hyperelliptic curvesKähler differentialscocyclesPollaczek polynomialsKrichever-Novikov algebrasuniversal central extensionuntwisted affine Kac-Moody algebraelliptic curve with punctures at two pointsKassel's theorem

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Elliptic curves (14H52) Differentials on Riemann surfaces (30F30)

Related Items (18)

Free field realizations of the elliptic affine Lie algebra \(\mathfrak{sl}(2, \mathbb R)\oplus (\varOmega_R/dR)\) ⋮ Krichever–Novikov Type Algebras. A General Review and the Genus Zero Case ⋮ Collective buckling of nonuniform nanobeams interacting through an elastic substrate ⋮ DJKM algebras and non-classical orthogonal polynomials ⋮ On the universal central extension of superelliptic affine Lie algebras ⋮ The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra ⋮ On Realizations of Some Plane Algebroid Curves ⋮ The three point gauge algebra \(\mathcal{V} \ltimes \mathfrak{sl}(2, \mathcal{R}) \oplus(\Omega_{\mathcal{R}} / d \mathcal{R})\) and its action on a Fock space ⋮ Certain families of polynomials arising in the study of hyperelliptic Lie algebras ⋮ The 3-point Virasoro algebra and its action on a Fock space ⋮ On the universal central extension of hyperelliptic current algebras ⋮ Representations for three-point Lie algebras of genus zero ⋮ DJKM algebras I: Their universal central extension ⋮ VERTEX ALGEBRAS ASSOCIATED WITH ELLIPTIC AFFINE LIE ALGEBRAS ⋮ The Sugawara construction and Casimir operators for Krichever-Novikov algebras ⋮ On the module structure of the center of hyperelliptic Krichever-Novikov algebras ⋮ Representations of Lie algebras ⋮ Free Field Realizations of the Date-Jimbo-Kashiwara-Miwa Algebra

Cites Work

• Krichever-Novikov algebras for more than two points
• Extended affine Lie algebras and their vertex representations
• Elliptic affine Lie algebras
• Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra
• Krichever-Novikov algebras for more than two points: explicit generators
• Central extensions and semi-infinite wedge representations of Krichever- Novikov algebras for more than two points
• Toroidal Lie algebras and vertex representations
• Universal central extensions of Chevalley algebras over Laurent polynomial rings and GIM Lie algebras
• Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons
• The arithmetic theory of loop groups
• Highest weight modules over certain quasigraded Lie algebras on elliptic curves
• On a Lie algebra of vector fields on a complex torus
• Toroidal groups¹
• Generalized Affine Kac-Moody Lie Algebras Over Localizations of the Polynomial Ring in One Variable

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