Four-Point Affine Lie Algebras

DOI10.2307/2160931zbMath0833.17023OpenAlexW4253596155MaRDI QIDQ4845919

Murray R. Bremner

Publication date: 12 March 1996

Full work available at URL: https://doi.org/10.2307/2160931

zbMATH Keywords

cocyclesKrichever-Novikov algebrascentral extensionaffine Kac-Moody algebrasultra spherical polynomials

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) Curves in algebraic geometry (14H99)

Related Items (15)

Krichever–Novikov Type Algebras. A General Review and the Genus Zero Case ⋮ On the universal central extension of superelliptic affine Lie algebras ⋮ The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra ⋮ Realizations of 𝐴₁⁽¹⁾-modules in category ̃𝒪 ⋮ 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 ⋮ On self-similar Lie algebras and virtual endomorphisms ⋮ The Sugawara construction and Casimir operators for Krichever-Novikov algebras ⋮ Representations of Lie algebras ⋮ From the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond ⋮ Free Field Realizations of the Date-Jimbo-Kashiwara-Miwa Algebra

Cites Work

• Krichever-Novikov algebras for more than two points
• Elliptic affine Lie algebras
• Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra
• Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons
• Central extensions of Lie algebras
• Cyclic homology of Dedekind domains
• Highest weight modules over certain quasigraded Lie algebras on elliptic curves
• Tensor Structures Arising from Affine Lie Algebras. I
• Generalized Affine Kac-Moody Lie Algebras Over Localizations of the Polynomial Ring in One Variable
• Cyclic homology of monogenic algebras
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