Biderivations of triangular algebras

Abstract

Naj bo ▫$\mathcal{A}$▫ trikotna algebra. Bilinearna preslikava ▫$\varphi \colon \mathcal{A \times A \rightarrow A}$▫ se imenuje biodvajanje, če je ▫$\varphi$▫ odvajanje glede na obe komponenti. V članku definiramo koncept ekstremalnega biodvajanja in dokažemo, da je ob določenih predpostavkah biodvajanje trikotne algebre ▫$\mathcal{A}$▫ vsota ekstremalnega biodvajanja in notranjega biodvajanja. Glavni izrek članka je nato uporabljen za opis biodvajanj (bločnih) zgornje trikotnih matričnih algeber in gnezdnih algeber. Prav tako je obravnavano tudi vprašanje, kdaj je odvajanje trikotne algebre notranje.

Keywords

matematika;trikotna algebra;trikotna matrična algebra;gnezdna algebra;biodvajanje;notranje biodvajanje;odvajanje;notranje odvajanje;mathematics;triangular algebra;triangular matrix algebra;nest algebra;biderivation;inner biderivation;derivation;inner derivation;

Data

Language:	English
Year of publishing:	2009
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552
COBISS:	15259481
ISSN:	0024-3795
Views:	952
Downloads:	63
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary title:	Biodvajanja trikotnih algeber
Secondary abstract:	Let ▫$\mathcal{A}$▫ be a triangular algebra. A bilinear map ▫$\varphi \colon \mathcal{A \times A \rightarrow A}$▫ is called a biderivation if it is a derivation with respect to both arguments. In this paper we define the concept of an extremal biderivation, and prove that under certain conditions a biderivation of a triangular algebra ▫$\mathcal{A}$▫ is a sum of an extremal and an inner biderivation. The main result is then applied to (block) upper triangular matrix algebras and nest algebras. We also consider the question when a derivation of a triangular algebra is an inner derivation.
Secondary keywords:	matematika;trikotna algebra;trikotna matrična algebra;gnezdna algebra;biodvajanje;notranje biodvajanje;odvajanje;notranje odvajanje;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1587-1602
Volume:	ǂVol. ǂ431
Issue:	ǂiss. ǂ9
Chronology:	2009
ID:	1474438