47 research outputs found

    Classification of simple weight modules for the N=2N=2 superconformal algebra

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    In this paper, we classify all simple weight modules with finite dimensional weight spaces over the N=2N=2 superconformal algebra.Comment: 18 pages, Latex, in this version we delete the Section 7 for application to the N=1N=1 superconformal algebr

    Heisenberg double of the generalized quantum euclidean group and its representations

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    The generalized quantum Euclidean group \oq(\frak{b}_{m,n}) is a natural generalization of the quantum Euclidean group \oq(\frak{b}_{1,1}). The Heisenberg double \od(\frak{b}_{m,n}) of \oq(\frak{b}_{m,n}) is the smash product of \oq(\frak{b}_{m,n}) with its Hopf dual \ou(\frak{b}_{m,n}). In this paper, we study the weight modules, the prime spectrum and the automorphism group of the Heisenberg double \od(\frak{b}_{m,n}).Comment: 11pages. comments are welcom

    Whittaker modules and hyperbolic Toda lattices

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    Let \sg be a complex finite-dimensional simple Lie algebra and let \sg_l be the corresponding generalized Takiff algebra. This paper studies the affine variety \ssf+\sb_l where \ssf is similar to a principal nilpotent element of \sg and \sb_l is a subalgebra corresponding to the Borel subalgebra \sb of \sg. Inspired by Kostant's work then we deal with two questions. One of them is to construct the Whittaker model for the GlG_l-invariants of symmetric algebra S(\sg_l) where GlG_l is the adjoint group of \sg_l and GlG_l acts on S(\sg_l) by coadjoint action, and then to classify all nonsingular Whittaker modules over \sg_l. Another one is to describe the symplectic structure of the manifold Z\subseteq\ssf+\sb_l of normalized Jacobi elements. Then the Hamiltonian corresponding to a fundamental invariant provides a class of hyperbolic Toda lattices. In particular, a simplest example describes the state of a dynamical system consisting of a positive mass particle and a negative mass particle.Comment: 45 page

    Introduction to co-split Lie algebras

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    In this work, we introduce a new concept which is obtained by defining a new compatibility condition between Lie algebras and Lie coalgebras. With this terminology, we describe the interrelation between the Killing form and the adjoint representation in a new perspective

    BL-MNE: Emerging Heterogeneous Social Network Embedding through Broad Learning with Aligned Autoencoder

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    Network embedding aims at projecting the network data into a low-dimensional feature space, where the nodes are represented as a unique feature vector and network structure can be effectively preserved. In recent years, more and more online application service sites can be represented as massive and complex networks, which are extremely challenging for traditional machine learning algorithms to deal with. Effective embedding of the complex network data into low-dimension feature representation can both save data storage space and enable traditional machine learning algorithms applicable to handle the network data. Network embedding performance will degrade greatly if the networks are of a sparse structure, like the emerging networks with few connections. In this paper, we propose to learn the embedding representation for a target emerging network based on the broad learning setting, where the emerging network is aligned with other external mature networks at the same time. To solve the problem, a new embedding framework, namely "Deep alIgned autoencoder based eMbEdding" (DIME), is introduced in this paper. DIME handles the diverse link and attribute in a unified analytic based on broad learning, and introduces the multiple aligned attributed heterogeneous social network concept to model the network structure. A set of meta paths are introduced in the paper, which define various kinds of connections among users via the heterogeneous link and attribute information. The closeness among users in the networks are defined as the meta proximity scores, which will be fed into DIME to learn the embedding vectors of users in the emerging network. Extensive experiments have been done on real-world aligned social networks, which have demonstrated the effectiveness of DIME in learning the emerging network embedding vectors.Comment: 10 pages, 9 figures, 4 tables. Full paper is accepted by ICDM 2017, In: Proceedings of the 2017 IEEE International Conference on Data Mining
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