Titlebook: Non-commutative and Non-associative Algebra and Analysis Structures; SPAS 2019, Västerås, Sergei Silvestrov,Anatoliy Malyarenko Conference

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,Index of Hom-Lie Algebras,The index is an important concept in representation theory and invariant theory. In this paper we extend the index theory to Hom-Lie algebras, we introduce the index theory in both cases, coadjoint and arbitrary representation. Moreover, we discuss Index of Multiplicative Simple Hom-Lie algebras and semidirect products of Hom-Lie algebras.

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Spectral Analysis of Equations over Quaternions,In this paper, we study how to solve certain equations on the set . of all quaternions. By using spectral analytic representations on ., monomial equations, some quadratic equations, and linear equations on . are considered.

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Multiplication and Linear Integral Operators on , Spaces Representing Polynomial Covariant Type ComRepresentations of polynomial covariant type commutation relations by pairs of linear integral operators and multiplication operators on Banach spaces . are constructed.

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Representations of Polynomial Covariance Type Commutation Relations by Piecewise Function MultiplicRepresentations of polynomial covariance type commutation relations are constructed on Banach spaces . and .. Representations involve operators of multiplication with piecewise functions, multiplication operators and inner superposition operators.

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978-3-031-32011-8The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Non-commutative and Non-associative Algebra and Analysis Structures978-3-031-32009-5Series ISSN 2194-1009 Series E-ISSN 2194-1017

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