A-Generators for the Dickson Algebra

1995 ◽  
Vol 347 (12) ◽  
pp. 4687 ◽  
Author(s):  
Nguyen H. V. Hu'ng ◽  
Franklin P. Peterson
Keyword(s):  
Dickson Algebra

A Note on Parabolic Subgroups and the Steenrod Algebra Action

2008 ◽  
Vol 15 (04) ◽  
pp. 689-698
Author(s):  
Nondas E. Kechagias
Keyword(s):  
Steenrod Algebra ◽  
Parabolic Subgroups ◽  
Generating Set ◽  
Modular Invariants ◽  
Dickson Algebra

The ring of modular invariants of parabolic subgroups has been described by Kuhn and Mitchell using Dickson algebra generators. We provide a new generating set which is closed under the Steenrod algebra action along with the relations between these elements.

On associative representations of non-associative algebras

2018 ◽  
Vol 17 (03) ◽  
pp. 1850051 ◽  
Author(s):  
A. I. Kornev ◽  
I. P. Shestakov
Keyword(s):  
Matrix Algebra ◽  
Poisson Algebra ◽  
Associative Algebras ◽  
The Matrix ◽  
Dickson Algebra

We define a notion of associative representation for algebras. We prove the existence of faithful associative representations for any alternative, Mal’cev, and Poisson algebra, and prove analogs of Ado-Iwasawa theorem for each of these cases. We construct also an explicit associative representation of the Cayley–Dickson algebra in the matrix algebra [Formula: see text]

scholarly journals The squaring operation on ${\cal A}$-generators of the Dickson algebra

2009 ◽  
Vol 85 (6) ◽  
pp. 67-70 ◽  
Author(s):  
Nguyên H. V. Hưng ◽  
Võ T. N. Quỳnh
Keyword(s):  
Dickson Algebra

scholarly journals $\scr A$-generators for the Dickson algebra

1995 ◽  
Vol 347 (12) ◽  
pp. 4687-4728 ◽  
Author(s):  
\textviet{Nguyễn H. V.} Hu’ng ◽  
Franklin P. Peterson
Keyword(s):  
Dickson Algebra

Spherical classes and the Dickson algebra

1998 ◽  
Vol 124 (2) ◽  
pp. 253-264 ◽  
Author(s):  
NGUYɘN H. V. HU'NG ◽  
FRANKLIN P. PETERSON
Keyword(s):  
Dickson Algebra

Orthogonality graphs of real Cayley–Dickson algebras. Part II: The subgraph on pairs of basis elements

2021 ◽  
pp. 1-35
Author(s):  
Svetlana Zhilina
Keyword(s):  
Standard Basis ◽  
Zero Divisors ◽  
Dickson Algebra

We consider zero divisors of an arbitrary real Cayley–Dickson algebra such that their components are both standard basis elements. We construct inductively the orthogonality graph on these elements. Then we show that, if we restrict our attention to at least [Formula: see text]-dimensional algebras, two algebras are isomorphic if and only if their graphs are isomorphic. We also provide an algorithm to retrieve the Cayley–Dickson parameters of an algebra from its graph.

Orthogonality graphs of real Cayley–Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons

2021 ◽  
pp. 1-27
Author(s):  
Svetlana Zhilina
Keyword(s):  
Main Sequence ◽  
Zero Divisor ◽  
Sufficient Conditions ◽  
Multiplication Table ◽  
Standard Basis ◽  
Sufficient Condition ◽  
Zero Divisor Graph ◽  
Zero Divisors ◽  
Necessary And Sufficient ◽  
Dickson Algebra

We study zero divisors whose components alternate strongly pairwise and construct oriented hexagons in the zero divisor graph of an arbitrary real Cayley–Dickson algebra. In case of the algebras of the main sequence, the zero divisor graph coincides with the orthogonality graph, and any hexagon can be extended to a double hexagon. We determine the multiplication table of the vertices of a double hexagon. Then we find a sufficient condition for three elements to generate an alternative subalgebra of an arbitrary Cayley–Dickson algebra. Finally, we consider those zero divisors whose components are both standard basis elements up to sign. We classify them and determine necessary and sufficient conditions under which two such elements are orthogonal.

scholarly journals Alternativity and reciprocity in the Cayley–Dickson algebra

2006 ◽  
Vol 39 (7) ◽  
pp. 1633-1644
Author(s):  
S Kuwata ◽  
H Fujii ◽  
A Nakashima
Keyword(s):  
Dickson Algebra

The Dickson Algebra

2021 ◽  
pp. 173-177
Author(s):  
Pavle V. M. Blagojević ◽  
Frederick R. Cohen ◽  
Michael C. Crabb ◽  
Wolfgang Lück ◽  
Günter M. Ziegler
Keyword(s):  
Dickson Algebra
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