共查询到20条相似文献,搜索用时 15 毫秒
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We canonically associate to any planar algebra two type II∞ factors M±. The subfactors constructed previously by the authors in Guionnet et al. (2010) [6] are isomorphic to compressions of M± to finite projections. We show that each M± is isomorphic to an amalgamated free product of type I von Neumann algebras with amalgamation over a fixed discrete type I von Neumann subalgebra. In the finite-depth case, existing results in the literature imply that M+≅M− is the amplification a free group factor on a finite number of generators. As an application, we show that the factors Mj constructed in Guionnet et al. (in press) [6] are isomorphic to interpolated free group factors L(F(rj)), rj=1+2δ−2j(δ−1)I, where δ2 is the index of the planar algebra and I is its global index. Other applications include computations of laws of Jones-Wenzl projections. 相似文献
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We give an example of a five-element unary algebra which is entropic but does not admit a natural duality.
Received September 26, 2000; accepted in final form April 4, 2001. 相似文献
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Georgia Benkart José M. Pé rez-Izquierdo 《Transactions of the American Mathematical Society》2000,352(2):935-968
Using the natural irreducible 8-dimensional representation and the two spin representations of the quantum group (D) of D, we construct a quantum analogue of the split octonions and study its properties. We prove that the quantum octonion algebra satisfies the q-Principle of Local Triality and has a nondegenerate bilinear form which satisfies a q-version of the composition property. By its construction, the quantum octonion algebra is a nonassociative algebra with a Yang-Baxter operator action coming from the R-matrix of (D). The product in the quantum octonions is a (D)-module homomorphism. Using that, we prove identities for the quantum octonions, and as a consequence, obtain at new ``representation theory' proofs for very well-known identities satisfied by the octonions. In the process of constructing the quantum octonions we introduce an algebra which is a q-analogue of the 8-dimensional para-Hurwitz algebra.
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V. G. Chernov 《Ukrainian Mathematical Journal》1990,42(3):331-336
We study the algebra of functions on the set of natural numbers with respect to the generalized convolution, generated by the generalized translation operator Tnf(k)=f(max (n, k)), n, k. With the help of the generalized Fourier transform, connected with this convolution, we establish numerous identities and recurrence relations, connecting, in particular, sums of powers of natural numbers.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 372–377, March, 1990. 相似文献
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Alberto Elduque 《Transactions of the American Mathematical Society》2004,356(10):3963-3983
The centralizer algebra of the action of on the real tensor powers of its natural module, , is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for and with the decomposition of into irreducible submodules is considered.
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Justyna Kosakowska 《数学学报(英文版)》2008,24(10):1687-1702
In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple Lie algebras. Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed. 相似文献
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G. Pisier 《Israel Journal of Mathematics》1979,34(1-2):38-44
We give an example of a strongly homogeneous Banach algebraB withA(T)⊊B⊊C(T) on which all 1-Lipschitzian functions operate; this improves previous results of M. Zafran. 相似文献
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Raymond Mortini 《Proceedings Mathematical Sciences》2009,119(5):629-634
We present a new and elementary approach to characterize the maximal ideals and their associated multiplicative linear functionals
for a classical real Banach algebra of analytic functions. 相似文献
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As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A 1 is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space. 相似文献
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J. Donald Monk 《Israel Journal of Mathematics》1980,35(1-2):135-150
A Boolean algebra is constructed having only those endomorphisms corresponding to prime ideals, which are present in any BA. The BA constructed is of powerc, has 2 c endomorphisms, and is not rigid in Bonnet’s sense. 相似文献
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Peter Schauenburg 《Proceedings of the American Mathematical Society》2004,132(4):965-972
We prove the quasi-Hopf algebra version of the Nichols-Zoeller theorem: A finite dimensional quasi-Hopf algebra is free over any quasi-Hopf subalgebra.
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This paper defines a remarkable Lie algebra of infinite dimension and rank, and conjectures that it may be related to the Fischer-Griess Monster group. 相似文献
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余德民 《纯粹数学与应用数学》2014,30(4):341-346
构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数. 相似文献
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We show that the Cuntz algebra can be represented as a crossed product of the canonical anticommutation relations algebra by an endomorphism. 相似文献