Related papers: Nil-clean companion matrices
We study the problem when every matrix over a division ring is representable as either the product of traceless matrices or the product of semi-traceless matrices, and also give some applications of such decompositions. Specifically, we…
For a complex nilpotent finite dimensional Lie algebra of matrices,and a Jordan-H\"older basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known…
We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.
This is survey of some recent results connecting random matrices, non-colliding processes and queues.
In this survey article, we summarise the known results towards the conjecture: elliptic curves over totally real number fields are modular. For understanding these recent results in the literature, we present some necessary background along…
We discuss aspects of recent novel approaches towards understanding the large N limit of matrix field theories with local or global non-abelian symmetry.
In this article, the concept of nil clean graph of a ring has been generalised to weakly nil clean graph of a ring and graph theoretic properties like girth, clique number, diameter and chromatic index of the graph have been studied for a…
The first author explicitly describes the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field in \cite{Ue17}. In this article, we generalize it over arbitrary characteristic fields. We also obtain a…
We study flat vector bundles over complex parallelizable manifolds.
We study the connectedness and the diameter of orthogonality graphs of upper triangular matrix algebras over arbitrary fields.
We study some classes of lazy cocycles, called pure (respectively neat), together with their categorical counterparts, entwined (respectively strongly entwined) monoidal categories.
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical algorithm to test nilpotency of…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
Interesting physical results can be obtained from sigma models by taking the number of fields N to zero. I discuss how one can make sense of this limit by using exact S matrix techniques. I review how this can be done for the case of…
By relating the two-dimensional U(N) Principal Chiral Model to a simple linear system we obtain a free-field parametrisation of solutions. Obvious symmetry transformations on the free-field data give symmetries of the model. In this way all…
A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.