3维Heisenberg李三系的自同构及Rota-Baxter算子

研究了3维Heisenberg李三系的自同构问题.给出了3维Heisenberg李三系的自同构、导子以及权为0和1的Rota-Baxter算子的矩阵表达式.

Rota-Baxter配对Lie模与Rota-Baxter配对Lie交叉模

首先引入Rota-Baxter配对Lie模概念,然后给出Rota-Baxter配对Lie模的一些构造,最后引入Rota-Baxter配对Lie交叉模概念,并在一个二维向量空间上构造Lie交叉模和Rota-Baxter配对算子.

由弱H-Hopf模代数构造Rota-Baxter代数

给出弱H-Hopf模代数的定义及其构造定理,进而由弱H-Hopf模代数出发构造Rota-Baxter代数并提供具体的例子。

Discussion on the Homology Theory of Lie Algebras

Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

Construction of Rota-Baxter algebras via Hopf module algebras

We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application,we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures.

Polylogarithms and multiple zeta values from free Rota-Baxter algebras

We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara,Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator.We apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single series.We also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.

Rota-Baxter Operators on 3-dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation

In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.

Rota-Baxter Operators of Weight 1 on 2×2-matrix Algebras

In this paper we determine all Rota-Baxter operators of weight 1 on 2 ×2- matrix algebras over an algebraically closed field.

Some results on derivations of MV-algebras

In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].

(ρ, τ, σ)-Derivations of Dendriform Algebras

We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.

2D Curves in Conformal Hyperquaternion Algebras H⊗2m

The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H⊗2m in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H⊗2m is the object of this work.

二维预约当代数的Rota-Baxter算子

本文主要计算二维预约当代数的Rota-Baxter算子,得到二维预约当代数上Rota-Baxter算子的完全分类。确定二维预约当代数对应的特殊的四维预约当代数的代数运算,构造这些特殊的四维预约当代数上JP-方程的解。最后利用二维预约当代数的Rota-Baxter算子构造二维的J-dendriform代数。

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

约当三系上非零权的相对Rota-Baxter算子

本文主要研究约当三系上关于非零权的相对Rota-Baxter算子。首先回顾了约当代数,约旦三系以及子系的概念,然后给出了约当三系的表示的定义,进而得出约当三系在另一个约当三系上作用的概念,以及约当三系上非零权的相对Rota-Baxter算子的定义,找到了在约当三系及其作用空间的直和上构造新约当三系的方法。最后,给出了在一个约当三系上定义与相对Rota-Baxter算子有关的新运算可得到新的约当三系的方法,并且构造了新的约当三系的表示。此外文中还给出了约当三系上构造相对Rota-Baxter算子的方法。

Root Systems Lie Algebras

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra

Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L2(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .

Split-Tetraquaternion Algebra and Applications

In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.

Quantum Computingvia Entanglement in Geometric Algebra Approach

The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.

The Report of Homological Algebra

The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules.