Results 101 to 110 of about 2,546 (128)
Some of the next articles are maybe not open access.
Quasi-pre-Lie bialgebras and twisting of pre-Lie algebras
Journal of Algebra and Its Applications, 2023Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra ([Formula: see text]-algebra). Then we study the twisting theory of (quasi-)twilled pre-Lie algebras and show that the result of the twisting by a linear map on a (quasi-)twilled pre-Lie algebra is also a (quasi-)twilled pre-Lie algebra if and only if the ...
Wang, Qi, Liu, Jiefeng
openaire +1 more source
On the pre-Lie algebra of specified Feynman graphs [PDF]
Journal of Mathematical Physics, 2019 We study the pre-Lie algebra of specified Feynman graphs ṼT and we define a pre-Lie structure on its doubling space F̃T. We prove that F̃T is pre-Lie module on ṼT and we find some relations between the two pre-Lie structures. Also, we study the enveloping algebras of two pre-Lie algebras denoted respectively by (D′̃T,★,Φ) and (H′̃T,⋆,Ψ) and we prove ...
Mohamed Belhaj Mohamed
exaly +3 more sources
2021
Pre-Lie algebras, also called Vinberg algebras, have become an important tool in combinatorics, differential geometry, the theory of operads and in various application domains such as perturbative quantum field theory or numerical analysis, to quote only a few.
Pierre Cartier, Frédéric Patras
openaire +1 more source
Pre-Lie algebras, also called Vinberg algebras, have become an important tool in combinatorics, differential geometry, the theory of operads and in various application domains such as perturbative quantum field theory or numerical analysis, to quote only a few.
Pierre Cartier, Frédéric Patras
openaire +1 more source
Algebra Colloquium, 2017
In this paper, we find Hall-Shirshov type bases for free pre-Lie algebras. We show that Segal’s basis of a free pre-Lie algebra is a type of these bases. We give a nonassociative Gröbner-Shirshov basis S for a free pre-Lie algebra such that Irr(S) is a monomial basis (called normal words) of a free pre-Lie algebra, where Irr(S) is the set of all ...
Li, Yu, Mo, Qiuhui
openaire +1 more source
In this paper, we find Hall-Shirshov type bases for free pre-Lie algebras. We show that Segal’s basis of a free pre-Lie algebra is a type of these bases. We give a nonassociative Gröbner-Shirshov basis S for a free pre-Lie algebra such that Irr(S) is a monomial basis (called normal words) of a free pre-Lie algebra, where Irr(S) is the set of all ...
Li, Yu, Mo, Qiuhui
openaire +1 more source
The Hopf Algebra of Fliess Operators and Its Dual Pre-lie Algebra [PDF]
Communications in Algebra, 2015 We study the Hopf algebra H of Fliess operators coming from Control Theory in the one-dimensional case. We prove that it admits a graded, finte-dimensional, connected gradation. Dually, the vector space IR is both a pre-Lie algebra for the pre-Lie product dual of the coproduct of H, and an associative, commutative algebra for the shuffle product. These
Loïc Foissy
exaly +4 more sources
On a Pre-Lie Algebra Defined by Insertion of Rooted Trees
Letters in Mathematical Physics, 2010A pre-Lie algebra is a vector space \(A\) with a binary operation \(*\) such that \(x*(y*z) - (x*y)*z = y*(x*z) - (y*x)*z\) for all \(x,y,z\) in \(A\). The free pre-Lie algebra with one generator is isomorphic to the vector space \(\mathcal T\) spanned by the rooted trees, endowed with the grafting Lie product [\textit{F.
exaly +3 more sources
Pre-Lie algebra characterization of SISO feedback invariants
53rd IEEE Conference on Decision and Control, 2014Transformation groups have been used extensively in system theory since its inception. Recently, a feedback transformation group for a nonlinear input-output system characterized by a Chen-Fliess functional expansion was described by the authors. In particular, an algorithm was given to identify a class of feedback invariant series.
W. Steven Gray +2 more
openaire +1 more source
Degenerations of Lie algebras and pre-Lie algebras
2011In dieser Arbeit beschÄftigen wir uns mit dem Orbitabschlussproblem fÜr Algebren in der Theorie der algebraischen Transformationsgruppen. Die allgemeine lineare Gruppe Gl(V) über einem Körper K operiert auf dem Vektorraum Alg(C), dem Raum aller K-Algebra-Strukturen, durch Basiswechsel.
openaire +1 more source
Journal of Geometry and Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
You Wang +3 more
openaire +2 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
You Wang +3 more
openaire +2 more sources
Cohomologies of Nijenhuis pre-Lie algebras and applications
Communications in AlgebraShuangjian Guo
exaly +2 more sources