Related papers: Introduction to Linear Bialgebra

Linear response theory is a tool with which one can study systems that are driven out of equilibrium by external perturbations. This monograph presents a thoroughly modern framework to make linear response theory rigorous for a wide array…

Lie admissible algebra structures, called center-symmetric algebras, are defined. Main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of…

We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…

We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14 which are not…

Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…

Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…

In this paper it is stressed that there is no {\em physical} reason for symmetries to be linear and that Lie group theory is therefore too restrictive. We illustrate this with some simple examples. Then we give a readable review on the…

We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we…

This paper introduces new ruled surfaces according to Bishop frame by referring to the main idea of Smarandache geometry. The fundamental forms and the corresponding curvatures are provided to put forth some characteristics of each surface.…

This paper studies bialgebraic structures associated with a Reynolds Leibniz algebra of weight $\lambda$, that is, a Leibniz algebra equipped with a Reynolds operator of weight $\lambda$. We first present equivalent characterizations of…

Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…

Study of soft sets was first proposed by Molodtsov in 1999 to deal with uncertainty in a non-parametric manner. The researchers did not pay attention to soft set theory at that time but now the soft set theory has been developed in many…

We introduce the concept of braided alternative bialgebra. The theory of cocycle bicrossproducts for alternative bialgebras is developed. As an application, the extending problem for alternative bialgebra is solved by using some non-abelian…

This paper extends topics in linear algebra and operator theory for linear transformations on complex vector spaces to those on bicomplex Hilbert and Banach spaces. For example, Definition 3 for the first time defines a bicomplex vector…

We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

We construct a bialgebra object in the category of linear maps LM from a cocommutative rack bialgebra. The construction does extend to some non-cocommutative rack bialgebras, as is illustrated by a concrete example. As a separate result, we…

Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…