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27
Vertex Lie algebras, vertex Poisson algebras and vertex algebras. In Recent developments in infinitedimensional Lie algebras and conformal field theory
 of Contemp. Math
, 2002
"... algebras ..."
Combinatorics of free vertex algebras
 J. Algebra
"... This paper illustrates the combinatorial approach to vertex algebra — study of vertex algebras presented by generators and relations. A necessary ingredient of this method is the notion of free vertex algebra. Borcherds [2] was the first to note that free vertex algebras do not exist in general. The ..."
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Cited by 9 (5 self)
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This paper illustrates the combinatorial approach to vertex algebra — study of vertex algebras presented by generators and relations. A necessary ingredient of this method is the notion of free vertex algebra. Borcherds [2] was the first to note that free vertex algebras do not exist in general. The
Identities of conformal algebras and pseudoalgebras
 Comm. Algebra
"... Abstract. For a given conformal algebra C, we write down the correspondence between identities of the coefficient algebra Coeff C and identities of C itself as of pseudoalgebra. In particular, we write down the defining relations of Jordan, alternative and Mal’cev conformal algebras, and show that t ..."
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Cited by 7 (7 self)
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Abstract. For a given conformal algebra C, we write down the correspondence between identities of the coefficient algebra Coeff C and identities of C itself as of pseudoalgebra. In particular, we write down the defining relations of Jordan, alternative and Mal’cev conformal algebras, and show that the analogue of Artin’s Theorem does not hold for alternative conformal algebras. 1. Conformal algebras In this note, we present a proof of a technical statement which concerns the relation between identities of a conformal algebra C and its coefficient algebra Coeff C. This relation was mentioned in [8], where some particular cases (associativity, commutativity, Jacobi identity) were considered. Although the approach of [8] is quite general, it is still technically difficult to write down the conformal identities corresponding to a given variety of ordinary algebras. We propose another approach which uses the language of pseudoproduct [1], in order to obtain the correspondence between identities of C and Coeff C in a very explicit form. This approach was mentioned in [1], where the most important
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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Cited by 7 (1 self)
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Abstract. We classify unital associative conformal algebras of linear growth and provide new examples of such.
ASSOCIATIVE CONFORMAL ALGEBRAS WITH FINITE FAITHFUL REPRESENTATION
, 2004
"... Abstract. We describe irreducible conformal subalgebras of CendN and build the structure theory of associative conformal algebras with finite faithful representation. 1. ..."
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Cited by 5 (5 self)
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Abstract. We describe irreducible conformal subalgebras of CendN and build the structure theory of associative conformal algebras with finite faithful representation. 1.
VARIETIES OF DIALGEBRAS AND CONFORMAL ALGEBRAS
, 2007
"... Abstract. For a given variety Var of algebras we define the variety Var of dialgebras. This construction turns to be closely related with varieties of pseudoalgebras: every Vardialgebra can be embedded into an appropriate pseudoalgebra of the variety Var. In particular, Leibniz algebras are exact ..."
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Cited by 4 (3 self)
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Abstract. For a given variety Var of algebras we define the variety Var of dialgebras. This construction turns to be closely related with varieties of pseudoalgebras: every Vardialgebra can be embedded into an appropriate pseudoalgebra of the variety Var. In particular, Leibniz algebras are exactly Lie dialgebras, and every Leibniz algebra can be embedded into current Lie conformal algebra.
Associative algebras related to conformal algebras
 Appl. Categ. Structures
"... Abstract. In this note, we introduce a class of algebras that are in some sense related to conformal algebras. This class (called TCalgebras) includes Weyl algebras and some of their (associative and Lie) subalgebras. By a conformal algebra we generally mean what is known as Hpseudoalgebra over t ..."
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Cited by 3 (2 self)
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Abstract. In this note, we introduce a class of algebras that are in some sense related to conformal algebras. This class (called TCalgebras) includes Weyl algebras and some of their (associative and Lie) subalgebras. By a conformal algebra we generally mean what is known as Hpseudoalgebra over the polynomial Hopf algebra H = k[T1,..., Tn]. Some recent results in structure theory of conformal algebras are applied to get a description of TCalgebras. 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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Cited by 2 (2 self)
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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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Cited by 2 (2 self)
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Abstract. We describe simple finitely generated associative conformal algebras of Gel’fand–Kirillov dimension one. 1.
On twisted representations of vertex algebras *
, 2002
"... In this paper we develop a formalism for working with representations of vertex and conformal algebras by generalized fields — formal power series involving noninteger powers of the variable. The main application of our technique is the construction of a large family of representations for the vert ..."
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Cited by 1 (0 self)
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In this paper we develop a formalism for working with representations of vertex and conformal algebras by generalized fields — formal power series involving noninteger powers of the variable. The main application of our technique is the construction of a large family of representations for the vertex superalgebra VΛ corresponding to an integer lattice Λ. For an automorphism ̂σ: VΛ → VΛ coming from a finite order automorphism σ: Λ→Λwe find the conditions for existence of twisted modules of VΛ. We show that the category of twisted representations of VΛ is semisimple with finitely many isomorphism classes of simple objects.