Pre-Poisson Algebras

By Marcelo Aguiar. 2000

308 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/756e3aa30186115830311a0f649b2ecd565bccfe

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In Algebra and Number Theory

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Citations in the corpus

NEW IDENTITIES IN DENDRIFORM ALGEBRAS (2007, methodology): “Following the work of M. Aguiar [ Agu00 ], the first author of the present article constructed then a forgetful functor from associative Rota–Baxter algebras to dendriform algebras, as well as various forgetful functors from dendriform algebras to other types of algebras [E02].”
Deformations of associative Rota-Baxter operators (2019, background): “Dendriform structures pay very much attention in the last 20 years due to its connection with Rota-Baxter algebras, shuffle algebras and combinatorics [2,19,28].”
Embedding of dendriform algebras into Rota-Baxter algebras (2011, background): “gebra should be deﬁned as x ⊢i y = R(x) ◦i y, x ⊣i y = x ◦i R(y), x ⊥i y = λx ◦i y. (15) It is easy to see that for λ 6= 0 one should just re-scale these binary operations to get (12). Proposition 6 ([1, 35]). Let B be an Ω-algebra with a Rota—Baxter operator R of weight λ = 0. Assume B belongs to V”
Splitting of operations, Manin products and Rota-Baxter operators (2011, background): “If we takeP to be the operad of associative algebras or the operad of Poisson algebras then we obtain the following results of Aguiar [2]: Corollary 5.2.”
On the algebra of quasi-shuffles (2005, background): “If we define a b := a · P(b), then one can check easily that (R, ,·) is a CTDalgebra, cf. [ 1 , 5, 7]. Moreover the operator P becomes an associative algebra morphism: P : (R, ) ! (R,·).”
Spitzer's identity and the algebraic Birkhoff decomposition in pQFT (2004, background): “For a ∈ A, inductively define (Ra) [n+1] := R((Ra) [n] a) and (Ra) {n+1} := R(a (Ra) {n} ) with the convention that (Ra) [ 1 ] = R(a) = (Ra) {1} and (Ra) [0] = 1 = (Ra) {0} . 8 To avoid possible confusion, we alert the reader that in [17] the concept of complete filtered Rota–Baxter algebras has bee”
On some anticyclic operads (2004, background): “Similarly, an anticyclic operad is an operad P together with an action of a symmetric group Sn+1 on P(n) extending the action of Sn and satisfying similar axioms.”
Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras (2019, background): “The following result captures the relationship between matching dendriform algebras and matching pre-Lie algebras, generalizing the well-known relationship between dendriform algebras and pre-Lie algebras [1].”
Nonabelian Generalized Lax Pairs, the Classical Yang-Baxter Equation and PostLie Algebras (2009, background): “If β : g → g is an intertwining operator on g, then it is also anaveraging operator [2, 42] in the Lie algebraic context, namely, [β(x), β(y)] = β([x, β(y)]) = β([β(x), y]), ∀x, y ∈ g, and is aNijenhuis tensor, namely, (24) [β(x), β(y)] + β(2)([x, y]) = β([β(x), y] + [x, β(y)]), ∀x, y ∈ g.”
FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES (2005, background): “Recently, there have been several interesting developments of Rota–Baxter algebras in theoretical physics and mathematics, including quantum field theory [12, 13, 43, 44, 51], associative Yang–Baxter equations [ 1 , 2], shuffle products [18, 36, 37], operads [4, 15, 19, 45, 46], Hopf algebras [6, 18”
On products and duality of binary, quadratic, regular operads (2004, background): “The first instance of such algebras, the dendriform dialgebra, has a string of two operators.”
Loday-Type Algebras and the Rota–Baxter Relation (2002, background): “Aguiar [13] to general Rota-Baxter operators including the link to dendriform trialgebras.”
Infinitesimal bialgebras, pre-Lie and dendriform algebras (2002, unknown): “We start by recalling a basic result from [ 2 ], which provides us with the examples of Baxter operators that are most relevant for our present purposes.”