We study the quantum N = 2 super-W3 algebra using the free field realization, which is obtained from the supersymmetric Miura transformation associated with the Lie superalgebra A(2|1). We compute the full operator product expansions of the algebra explicitly. It is found that the results agree with those obtained by the OPE method. ∗Address after March 1, 1993: Institute of Physics, University...

Provenance is well-understood for relational query operators. Increasingly, however, data analytics is incorporating operations expressed through linear algebra: machine learning operations, network centrality measures, and so on. In this paper, we study provenance information for matrix data and linear algebra operations. Our core technique builds upon provenance for aggregate queries and cons...

There are several factorizations of multidimensional tensors into lower-dimensional components, known as “tensor networks.” We consider the popular “tensor-train” (TT) format and ask, How efficiently can we compute a low-rank approximation from full tensor on current multicore CPUs? Compared to sparse dense linear algebra, kernel libraries for multilinear algebra rare typically not well optimiz...

We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley–Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that M1,M2 ∈ L =⇒ M1M2 − M2M1 ∈ L. Two matrix Lie algebras are conjugate if there is an invertible matrix M such that L1 = ML...

The use of linear algebra routines is fundamental to many areas of computational science, yet their implementation in software still forms the main computational bottleneck in many widely used algorithms. In machine learning and computational statistics, for example, the use of Gaussian distributions is ubiquitous, and routines for calculating the Cholesky decomposition, matrix inverse and matr...

A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations. Abstract A generalization of the Yang-Baxter algebra is found in quantizing the mon-odromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in involution which form t...