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Associative conformal algebras of linear growth
 J. Algebra
"... Abstract. We classify unital associative conformal algebras of linear growth and provide new examples of such. ..."
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Abstract. We classify unital associative conformal algebras of linear growth and provide new examples of such.
Parking functions and vertex operators
"... Abstract. We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations of symmetric groups which turn out to be isomorphic ..."
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Abstract. We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations of symmetric groups which turn out to be isomorphic to parking function modules. We also construct series of vector spaces whose dimensions are Catalan numbers and Fuss–Catalan numbers respectively. Conjecturally, these spaces are related to spaces of global sections of vector bundles on (zero fibres of) Hilbert schemes and representations of rational Cherednik algebras. 1.
SIMPLE ASSOCIATIVE CONFORMAL ALGEBRAS OF LINEAR GROWTH
, 2004
"... Abstract. We describe simple finitely generated associative conformal algebras of Gel’fand–Kirillov dimension one. 1. ..."
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Abstract. We describe simple finitely generated associative conformal algebras of Gel’fand–Kirillov dimension one. 1.
Invariant bilinear forms on a vertex algebra
 J. Pure Appl. Algebra
"... Invariant bilinear forms on vertex algebras have been around for quite some time now. They were mentioned by Borcherds in [1] and were used in many early works on vertex algebras, especially in relation with the vertex algebras associated with lattices [2, 3, 8]. The first systematic study of invari ..."
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Invariant bilinear forms on vertex algebras have been around for quite some time now. They were mentioned by Borcherds in [1] and were used in many early works on vertex algebras, especially in relation with the vertex algebras associated with lattices [2, 3, 8]. The first systematic study of invariant forms on vertex algebras is due to Frenkel, Huang and Lepowsky [7]. This theory was
ON EMBEDDING OF LIE CONFORMAL ALGEBRAS INTO ASSOCIATIVE CONFORMAL ALGEBRAS
, 2004
"... Conformal algebras. A conformal algebra is, roughly speaking, a linear space A with infinitely many bilinear products (n) : A × A → A, parameterized by an nonnegative integer n, and a derivation D: A → A. An important property of these products is that for any fixed a, b ∈ A we have a(n)b = 0 when ..."
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Conformal algebras. A conformal algebra is, roughly speaking, a linear space A with infinitely many bilinear products (n) : A × A → A, parameterized by an nonnegative integer n, and a derivation D: A → A. An important property of these products is that for any fixed a, b ∈ A we have a(n)b = 0 when n is large enough. See section §1 below for formal definitions.
A NOTE ON INVARIANT BILINEAR FORMS ON A VERTEX ALGEBRA
, 2002
"... Invariant bilinear forms on vertex algebras have been around for quite some time now. They were mentioned by Borcherds in [1] and were used in many early works on vertex algebras, especially in relation with the vertex algebras associated with lattices [2, 3, 7]. The first systematic study of invari ..."
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Invariant bilinear forms on vertex algebras have been around for quite some time now. They were mentioned by Borcherds in [1] and were used in many early works on vertex algebras, especially in relation with the vertex algebras associated with lattices [2, 3, 7]. The first systematic study of invariant forms on vertex algebras is due to Frenkel, Huang and Lepowsky [6]. This theory was
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.
A UNIVERSAL APPROACH TO VERTEX ALGEBRAS
"... The notion of vertex algebra due to Borcherds [3] and FrenkelLepowskyMeurman [8] is one of the fundamental concepts of modern mathematics. The definition is purely algebraic, but its central point of the is an intricate Jacobi identity ([8]), which makes the definition hard to motivate from first ..."
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The notion of vertex algebra due to Borcherds [3] and FrenkelLepowskyMeurman [8] is one of the fundamental concepts of modern mathematics. The definition is purely algebraic, but its central point of the is an intricate Jacobi identity ([8]), which makes the definition hard to motivate from first principles. The identity can
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