共查询到20条相似文献,搜索用时 743 毫秒
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We construct an associative product on the symmetric module of any pre-Lie algebra L. It turns into a Hopf algebra which is isomorphic to the envelopping algebra of . Then we prove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees. To cite this article: J.-M. Oudom, D. Guin, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as , , or , where . In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras. 相似文献
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If a vertex operator algebra satisfies , , then has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set of symmetric matrices of degree d becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, central charges influence the properties of vertex operator algebras. In this paper, we construct vertex operator algebras with central charge c and its Griess algebra is isomorphic to for any complex number c and a positive integer d. 相似文献
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Max Karoubi 《Comptes Rendus Mathematique》2005,341(6):339-342
In this Note, we introduce a new morphism between algebraic and hermitian K-theory. The topological analog is the Adams operation in real K-theory. From this morphism, we deduce a lower bound for the higher algebraic K-theory of a ring A in terms of the classical Witt group of the ring . To cite this article: M. Karoubi, C. R. Acad. Sci. Paris, Ser. I 341 (2005). 相似文献
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Takeshi Suzuki 《Comptes Rendus Mathematique》2006,343(6):383-386
We study a class of representations called ‘calibrated representations’ of the rational and trigonometric double affine Hecke algebras of type . We give a realization of calibrated irreducible modules as spaces of coinvariants constructed from integrable modules over the affine Lie algebra . We also give a character formula of these irreducible modules in terms of a generalization of Kostka polynomials. These results are conjectured by Arakawa, Suzuki and Tsuchiya based on the conformal field theory. The proofs using recent results on the representation theory of the double affine Hecke algebras will be presented in the forthcoming papers. To cite this article: T. Suzuki, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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Gaywalee Yamskulna 《Journal of Algebra》2009,321(3):1005-1015
In this paper we prove that the vertex algebra is rational if L is a negative definite even lattice of finite rank, or if L is a non-degenerate even lattice of a finite rank that is neither positive definite nor negative definite. In particular, for such even lattices L, we show that the Zhu algebras of the vertex algebras are semisimple. This extends the result of Abe from [T. Abe, Rationality of the vertex operator algebra for a positive definite even lattice L, Math. Z. 249 (2) (2005) 455–484] which establishes the rationality of when L is a positive definite even lattice of finite rank. 相似文献
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We show that the Kashiwara–Vergne (KV) problem for quadratic Lie algebras (that is, Lie algebras admitting an invariant scalar product) reduces to the problem of representing the Campbell–Hausdorff series in the form , where and are Lie series in x and y. This observation explains the existence of explicit rational solutions of the quadratic KV problem, whereas constructing an explicit rational solution of the full KV problem would probably require the knowledge of a rational Drinfeld associator. It also gives, in the case of quadratic Lie algebras, a direct proof of the Duflo theorem (implied by the KV problem). To cite this article: A. Alekseev, C. Torossian, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
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《Indagationes Mathematicae》2017,28(2):390-405
In this paper, we consider equations of Lie triple algebras that are train algebras. We obtain two different types of equations depending on assuming the existence of an idempotent or a pseudo-idempotent.In general Lie triple algebras are not power-associative. However we show that their train equation with an idempotent is similar to train equations of power-associative algebras that are train algebras and we prove that Lie triple algebras that are train algebras of rank with an idempotent are Jordan algebras.Moreover, the set of non-trivial idempotents has the same expression in Peirce decomposition as that of -stable power-associative algebras.We also prove that the algebra obtained by -gametization process of a Lie triple algebra is a Lie triple one. 相似文献