�ber Invarianten in Lie'schen Ringen

Wever, Franz

doi:10.1007/bf01447846

Cited by 47 publications

(31 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We recover in particular the theorem of Dynkin [3], Specht [19], Wever [20] (case f = Id) and obtain an extension thereof to the case f = δ x i . We let the reader derive similar results for other families of Lie derivations.…”

Section: Corollary 2 For a Lie Derivation δ The Map D δ Maps T (X)mentioning

confidence: 72%

Logarithmic derivatives and generalized Dynkin operators

Menous¹,

Patras²

2013

J Algebr Comb

View full text Add to dashboard Cite

Motivated by a recent surge of interest for Dynkin operators in mathematical physics and by problems in the combinatorial theory of dynamical systems, we propose here a systematic study of logarithmic derivatives in various contexts. In particular, we introduce and investigate generalizations of the Dynkin operator for which we obtain Magnus-type formulas.Keywords Dynkin operator · Free Lie algebras · Logarithmic derivative · Rota-Baxter algebra IntroductionDynkin operators are usually defined as iterated bracketings. They are particularly popular in the framework of linear differential equations and the so-called continuous Baker-Campbell-Hausdorff problem (to compute the logarithm of an evolution operator). We refer to [17] for details and an historical survey of the field. Dynkin operators can also be expressed as a particular type of logarithmic derivatives (see Corollary 3 below). They have received increasingly more and more interest during recent years, for various reasons.(1) In the theory of free Lie algebras and noncommutative symmetric functions, it was shown that Dynkin operators generate the descent algebra (the direct sum of Solomon's algebras of type A, see [9,17]) and play a crucial role in the theory of Lie idempotents.

show abstract

Section: Corollary 2 For a Lie Derivation δ The Map D δ Maps T (X)mentioning

confidence: 72%

Logarithmic derivatives and generalized Dynkin operators

Menous¹,

Patras²

2013

J Algebr Comb

View full text Add to dashboard Cite

show abstract

“…For each positive integer n, let L n (V ) be the homogeneous component of L(V ) of degree n. Then L(V ) and L n (V ) are themselves KG-modules, and these modules have been studied intensively over the past 50 years. We mention the pioneering work of Thrall [12], Brandt [2] and Wever [14], and for an account of some of the later work we refer to [9]. Most of the results on the module structure of L(V ) are concerned with the case where K is a field of characteristic zero, and very little seems to be known for prime characteristic.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

On the module structure of free Lie algebras

Bryant

Stöhr

1999

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Обобщенное тождество Якоби для n = 4 обсуждалось в работе [14] и имеет вид В общем случае для любой ассоциативной алгебры имеем следующие тождества:…”

Section: обобщение основных тождествunclassified