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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.
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
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.
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 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
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 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 ..."
Abstract
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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