Matches in SemOpenAlex for { <https://semopenalex.org/work/W4298114117> ?p ?o ?g. }
Showing items 1 to 49 of
49
with 100 items per page.
- W4298114117 abstract "Let A be an associative algebra (or any other kind of algebra for that matter). A derivation on A is an endomorphism del of the underlying Abelian group of A such that del(ab)=a(del b)+(del a)b for all a,bin A (1.1) A Hasse-Schmidt derivation is a sequence (d_0=id,d_1,d_2,...,d_n,...) of endomorphisms of the underlying Abelian group such that for all n ge 1 d_n(ab)= sum_{i=0}^n (d_ia)(d_{n-i}b) (1.2) Note that d_1 is a derivation as defined by (1.1). The individual d_n that occur in a Hasse-Schmidt derivation are also sometimes called higher derivations. A question of some importance is whether Hasse-Schmidt derivations can be written down in terms of polynomials in ordinary derivations. For instance in connection with automatic continuity for Hasse-Schmidt derivations on Banach algebras. Such formulas have been written down by, for instance, Heerema and Mirzavaziri in [5] and [6]. They also will be explicitly given below. It is the purpose of this short note to show that such formulas follow directly from some easy results about the Hopf algebra NSymm of non-commutative symmetric functions. In fact this Hopf algebra constitutes a universal example concerning the matter." @default.
- W4298114117 created "2022-10-01" @default.
- W4298114117 creator A5088746467 @default.
- W4298114117 date "2011-10-13" @default.
- W4298114117 modified "2023-09-24" @default.
- W4298114117 title "Hasse-Schmidt derivations and the Hopf algebra of noncommutative symmetric functions" @default.
- W4298114117 doi "https://doi.org/10.48550/arxiv.1110.6108" @default.
- W4298114117 hasPublicationYear "2011" @default.
- W4298114117 type Work @default.
- W4298114117 citedByCount "0" @default.
- W4298114117 crossrefType "posted-content" @default.
- W4298114117 hasAuthorship W4298114117A5088746467 @default.
- W4298114117 hasBestOaLocation W42981141171 @default.
- W4298114117 hasConcept C116858840 @default.
- W4298114117 hasConcept C13355873 @default.
- W4298114117 hasConcept C136119220 @default.
- W4298114117 hasConcept C136170076 @default.
- W4298114117 hasConcept C183778304 @default.
- W4298114117 hasConcept C202444582 @default.
- W4298114117 hasConcept C2524010 @default.
- W4298114117 hasConcept C29712632 @default.
- W4298114117 hasConcept C33923547 @default.
- W4298114117 hasConcept C68797384 @default.
- W4298114117 hasConceptScore W4298114117C116858840 @default.
- W4298114117 hasConceptScore W4298114117C13355873 @default.
- W4298114117 hasConceptScore W4298114117C136119220 @default.
- W4298114117 hasConceptScore W4298114117C136170076 @default.
- W4298114117 hasConceptScore W4298114117C183778304 @default.
- W4298114117 hasConceptScore W4298114117C202444582 @default.
- W4298114117 hasConceptScore W4298114117C2524010 @default.
- W4298114117 hasConceptScore W4298114117C29712632 @default.
- W4298114117 hasConceptScore W4298114117C33923547 @default.
- W4298114117 hasConceptScore W4298114117C68797384 @default.
- W4298114117 hasLocation W42981141171 @default.
- W4298114117 hasOpenAccess W4298114117 @default.
- W4298114117 hasPrimaryLocation W42981141171 @default.
- W4298114117 hasRelatedWork W1990993134 @default.
- W4298114117 hasRelatedWork W2005124234 @default.
- W4298114117 hasRelatedWork W2006990530 @default.
- W4298114117 hasRelatedWork W2066904167 @default.
- W4298114117 hasRelatedWork W2071709946 @default.
- W4298114117 hasRelatedWork W2072721116 @default.
- W4298114117 hasRelatedWork W2118316830 @default.
- W4298114117 hasRelatedWork W2789923144 @default.
- W4298114117 hasRelatedWork W2951853154 @default.
- W4298114117 hasRelatedWork W4240632147 @default.
- W4298114117 isParatext "false" @default.
- W4298114117 isRetracted "false" @default.
- W4298114117 workType "article" @default.