47 research outputs found
Classification of simple weight modules for the superconformal algebra
In this paper, we classify all simple weight modules with finite dimensional
weight spaces over the superconformal algebra.Comment: 18 pages, Latex, in this version we delete the Section 7 for
application to the 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
Whittaker modules and hyperbolic Toda lattices
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 -invariants of
symmetric algebra S(\sg_l) where is the adjoint group of \sg_l and
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
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