Meta-Invariant Operators over Cayley-Dickson Algebras and Spectra

Lüdkovsky, S. V.

doi:10.4236/apm.2013.31008

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…There are many papers devoted to the study of the roots of polynomial equations with coefficients in A t . In [10], the author studied zeros of polynomials over Cayley-Dickson algebras, without providing a clear algorithm to find them. In the papers [11][12][13][14][15][16][17][18][19] the authors studied roots of quaternionic and octonionic polynomials and provided laboriously methods to find these roots.…”

Section: A Quadratic Equation Over Real Quaternionsmentioning

confidence: 99%

Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications

Flaut

Zaharia

2022

Mathematics

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Due to the computational aspects which appear in the study of algebras obtained by the Cayley–Dickson process, it is difficult to obtain nice properties for these algebras. For this reason, finding some identities in such algebras plays an important role in obtaining new properties of these algebras and facilitates computations. In this regard, in the first part of this paper, we present some new identities and properties in algebras obtained by the Cayley–Dickson process. As another remark regarding the computational aspects in these algebras, in the last part of this paper, we solve some quadratic equations in the real division quaternion algebra when their coefficients are some special elements. These special coefficients allowed us to solve interesting quadratic equations, providing solutions directly, without using specialized softs.

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Section: A Quadratic Equation Over Real Quaternionsmentioning

confidence: 99%

Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications

Flaut

Zaharia

2022

Mathematics

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Completions and homomorphisms of infinite dimensional Cayley–Dickson algebras

Lüdkovsky

2019

Linear and Multilinear Algebra

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Decomposition of modules over generalized Dickson algebras

Ludkovsky

2024

Russian Universities Reports. Mathematics

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The article is devoted to modules over generalized Dickson algebras. These algebras are nonassociative and generally can be nonalternative. They compose an important class of algebras and an area in mathematics. Left, right and two-sided modules over generalized Dickson algebras are studied. Their structure and submodules are investigated. Bimodules with involution are scrutinized over generalized Dickson algebras with involution. Such bimodules have specific features caused by involution. Minimal submodules and decomposition of modules are investigated. In particular, cyclic submodules are studied.

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Meta-Invariant Operators over Cayley-Dickson Algebras and Spectra

Abstract: A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. Moreover, theorems about spectra of generalized unitary operators and their semigroups are demonstrated.

Cited by 3 publications

References 23 publications

Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications

Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications

Completions and homomorphisms of infinite dimensional Cayley–Dickson algebras

Decomposition of modules over generalized Dickson algebras

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