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

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

Heisenberg double of the generalized quantum euclidean group and its representations

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

Introduction to co-split Lie algebras

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

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

Quantum N-toroidal algebras and extended quantized GIM algebras of N-fold affinization

We introduce the notion of quantum $N$-toroidal algebras uniformly as a natural generalization of the quantum toroidal algebras as well as extended quantized GIM algebras of $N$-fold affinization. We show that the quantum $N$-toroidal algebras are quotients of the extended quantized GIM algebras of $N$-fold affinization, which generalizes a well-known result of Berman and Moody for Lie algebras. Moreover, we construct a level-one vertex representation of the quantum $N$-toroidal algebra for type $A$.Comment: 3