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Constructions of vertex operator coalgebras via vertex operator algebras
"... Abstract. The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions of one string propagating in spacetime splitting into n strings in conformal field theory. This notion is in some sense dual to the notion of vertex operator algebra. We prove tha ..."
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Abstract. The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions of one string propagating in spacetime splitting into n strings in conformal field theory. This notion is in some sense dual to the notion of vertex operator algebra. We prove that any vertex operator algebra equipped with a nondegenerate, Virasoro preserving, bilinear form gives rise to a corresponding vertex operator coalgebra. 1.
VERTEX COALGEBRAS, COMODULES, COCOMMUTATIVITY AND COASSOCIATIVITY
, 801
"... Abstract. We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skewsymmetry, and an endomorphism, D ∗ , which hold on vertex coalgebras. The former two properties require grading. We then discuss ..."
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Abstract. We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skewsymmetry, and an endomorphism, D ∗ , which hold on vertex coalgebras. The former two properties require grading. We then discuss comodule structure. We conclude by discussing instances where graded vertex coalgebras appear, particularly as related to Primc’s vertex Lie algebra and (universal) enveloping vertex algebras. 1.
ON GRIESS ALGEBRAS
, 2006
"... Abstract. In this paper we prove that for any commutative (but in general nonassociative) algebra A with an invariant symmetric nondegenerate bilinear form there is a graded vertex algebra V = V0 ⊕ V1 ⊕ V2 ⊕..., such that dim V0 = 1, V1 = 0 and V2 contains A. We can choose V so that if A has a uni ..."
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Abstract. In this paper we prove that for any commutative (but in general nonassociative) algebra A with an invariant symmetric nondegenerate bilinear form there is a graded vertex algebra V = V0 ⊕ V1 ⊕ V2 ⊕..., such that dim V0 = 1, V1 = 0 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V has a nondegenerate invariant bilinear form, and therefore is simple.
Symmetry, Integrability and Geometry: Methods and Applications On Griess Algebras ⋆
"... Abstract. In this paper we prove that for any commutative (but in general nonassociative) algebra A with an invariant symmetric nondegenerate bilinear form there is a graded vertex algebra V = V0 ⊕ V2 ⊕ V3 ⊕ · · · , such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit ..."
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Abstract. In this paper we prove that for any commutative (but in general nonassociative) algebra A with an invariant symmetric nondegenerate bilinear form there is a graded vertex algebra V = V0 ⊕ V2 ⊕ V3 ⊕ · · · , such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a nondegenerate invariant bilinear form, in which case it is simple. Key words: vertex algebra; Griess algebra
Constructions of VERTEX OPERATOR ALGEBRAS via VERTEX OPERATOR ALGEBRAS
, 2005
"... The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions modeling one string propagating in spacetime splitting into n strings in conformal field theory. This notion is in some sense dual to the notion of vertex operator algebra. We prove that ..."
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The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions modeling one string propagating in spacetime splitting into n strings in conformal field theory. This notion is in some sense dual to the notion of vertex operator algebra. We prove that any vertex operator algebra equipped with a nondegenerate, Virasoro preserving, bilinear form gives rise to a corresponding vertex operator coalgebra. We then explicitly calculate the vertex operator coalgebra structure and unique bilinear form for the Heisenberg algebra case, which corresponds to considering free bosons in conformal field theory.
Research Statement
"... operator algebra theory. My dissertation examines the coalgebraic structure arising from the geometry of genuszero worldsheets in conformal field theory. I would like to continue this work and am particularly interested in extending the known structure of vertex operator algebras and their represen ..."
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operator algebra theory. My dissertation examines the coalgebraic structure arising from the geometry of genuszero worldsheets in conformal field theory. I would like to continue this work and am particularly interested in extending the known structure of vertex operator algebras and their representations to bialgebraic