Peirce decompositions and Jordan matrix algebras

1968 ◽  
pp. 117-151
Keyword(s):  
Matrix Algebras ◽  
Jordan Matrix

scholarly journals Reduced Jordan matrix algebras over complete local rings

1978 ◽  
Vol 81 (1) ◽  
pp. 97-109
Author(s):  
Holger P. Petersson
Keyword(s):  
Local Rings ◽  
Matrix Algebras ◽  
Jordan Matrix

Tensor Products of Jordan Algebras

1975 ◽  
Vol 27 (1) ◽  
pp. 60-74 ◽  
Author(s):  
Aubrey Wulfsohn
Keyword(s):  
Tensor Product ◽  
Jordan Algebra ◽  
Kronecker Product ◽  
Tensor Products ◽  
Jordan Algebras ◽  
Mapping Property ◽  
Associative Algebras ◽  
Matrix Algebras ◽  
Special Jordan Algebra ◽  
Jordan Matrix

Let J1 and J2 be two Jordan algebras with unit elements. We define various tensor products of J1 and J2. The first, which we call the Kronecker product, is the most obvious and is based on the tensor product of the vector spaces. We find conditions sufficient for its existence and for its non-existence. Motivated by the universal mapping property for the tensor product of associative algebras we define, in Section 2, tensor products of J1 and J2 by means of a universal mapping property. The tensor products always exist for special Jordan algebras and need not coincide with the Kronecker product when the latter exists. In Section 3 we construct a more concrete tensor product for special Jordan algebras. Here the tensor product of a special Jordan algebra and an associative Jordan algebra coincides with the Kronecker product of these algebras. We show that this "special" tensor product is the natural tensor product for some Jordan matrix algebras.

Jordan derivation of certain Jordan matrix algebras

2008 ◽  
Vol 56 (5) ◽  
pp. 581-588 ◽  
Author(s):  
Dengyin Wang ◽  
Qian Hu ◽  
Chunguang Xia
Keyword(s):  
Jordan Derivation ◽  
Matrix Algebras ◽  
Jordan Matrix

scholarly journals Local derivations on associative and Jordan matrix algebras

2019 ◽  
Vol 2019 (4) ◽  
pp. 23-36
Author(s):  
Sh.A. Ayupov ◽  
F.N. Arzikulov ◽  
N.M. Umrzaqov
Keyword(s):  
Matrix Algebras ◽  
Jordan Matrix

scholarly journals The isotopy problem for Jordan matrix algebras

1978 ◽  
Vol 244 ◽  
pp. 185-185 ◽  
Author(s):  
Holger P. Petersson
Keyword(s):  
Matrix Algebras ◽  
Jordan Matrix

scholarly journals On Prime Goldie-Like Quadratic Jordan Matrix Algebras(1)

1977 ◽  
Vol 20 (1) ◽  
pp. 39-45 ◽  
Author(s):  
Daniel J. Britten
Keyword(s):  
Jordan Algebra ◽  
General Setting ◽  
Jordan Algebras ◽  
Matrix Algebras ◽  
Jordan Matrix

In [1] and [2], there was given a characterization for linear Jordan matrix algebras whose coordinatizing ring is *-prime Goldie or a Cayley-Dickson ring (C-D ring). If one considers the corresponding question in the more general setting of quadratic Jordan algebra as defined by McCrimmon in [11], then the result is similar. In this latter case the ample quadratic Jordan algebras, as studied by Montgomery in [12] and [13], are brought into play.

scholarly journals Jordan matrix algebras defined by generators and relations

2021 ◽  
Vol 7 (2) ◽  
pp. 3047-3055
Author(s):  
Yingyu Luo ◽  
◽  
Yu Wang ◽  
Junjie Gu ◽  
Huihui Wang ◽  
...  
Keyword(s):  
Generators And Relations ◽  
Matrix Algebras ◽  
Number Of Generators ◽  
Jordan Matrix

<abstract><p>In the present paper we describe Jordan matrix algebras over a field by generators and relations. We prove that the minimun number of generators of some special Jordan matrix algebras over a field is $ 2 $.</p></abstract>

Notes on three-pass protocol

2020 ◽  
Vol 25 (4) ◽  
pp. 4-9
Author(s):  
Yerzhan R. Baissalov ◽  
Ulan Dauyl
Keyword(s):  
Finite Fields ◽  
Matrix Algebras ◽  
Associative Structures

The article discusses primitive, linear three-pass protocols, as well as three-pass protocols on associative structures. The linear three-pass protocols over finite fields and the three-pass protocols based on matrix algebras are shown to be cryptographically weak.

τ-tilting finite triangular matrix algebras

2021 ◽  
pp. 106785
Author(s):  
Takuma Aihara ◽  
Takahiro Honma
Keyword(s):  
Triangular Matrix ◽  
Matrix Algebras

scholarly journals Iterants, Majorana Fermions and the Majorana-Dirac Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1373
Author(s):  
Louis H. Kauffman
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Clifford Algebras ◽  
Discrete Systems ◽  
Complex Numbers ◽  
Majorana Fermions ◽  
Matrix Algebras ◽  
Dirac Equations ◽  
Points Of View

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.

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