Related papers: On L-dendriform conformal algebras
In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a…
This article gives a brief introduction to some recent work on deformation and homotopy theories of Rota-Baxter operators and more generally $\mathcal{O}$-operators on Lie algebras, by means of the differential graded Lie algebra approach.…
In this paper, we introduce the definition of pre-Gel'fand-Dorfman algebra and present several constructions. Moreover, we show that a class of left-symmetric conformal algebras named quadratic left-symmetric conformal algebras are one to…
We introduce the notion of quasi-triangular anti-dendriform bialgebras, which can be induced by the solutions of the AD-YBE whose symmetric parts are invariant. A factorizable anti-dendriform bialgebra leads to a factorization of the…
In this paper we fill some gaps in the arguments of our previous papers [hep-th/9412229,hep-th/9604044]. In particular, we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining relations of the Yang-Baxter…
We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…
This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra, defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra…
A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$. Using Voronov's derived bracket and a recent work of Lazarev et al., we construct an…
A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional rationality (or meromorphicity) conditions…
In this paper, we introduce the notion of curved $\mathcal{O}$-operator systems as a generalization of T. Brzezi\'{n}ski's (curved) Rota-Baxter systems, and then investigate their relations with $\mathcal{O}$-operator systems,…
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…
From the `cofree' cooperad $T'(A[-1])$ on a collection $A$ together with a differential, we construct an $L_\infty$-algebra structure on the total space $\bigoplus_nA(n)$ that descends to coinvariants. We use this construction to define an…
We establish a bialgebra structure on Rota-Baxter Lie algebras following the Manin triple approach to Lie bialgebras. Explicitly, Rota-Baxter Lie bialgebras are characterized by generalizing matched pairs of Lie algebras and Manin triples…
The main purpose of this paper is to introduce and investigate the notion of Jacobi-Jordan conformal algebra. They are a generalization of Jacobi-Jordan algebras which correspond to the case in which the formal parameter lambda equals 0. We…
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
We introduce the notion of Leibniz conformal bialgebras, presenting a bialgebra theory for Leibniz conformal algebras as well as the conformal analogues of Leibniz bialgebras. They are equivalently characterized in terms of matched pairs…
In this paper, we mainly discuss how to use dendriform $\md$-bialgebras to construct Lie bialgebras and the relationship between the solutions of their corresponding Yang-Baxter equations. We provide two methods for obtaining Lie algebras…
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…
We introduce a notion of oriented dialgebra and develop a cohomology theory for oriented dialgebras based on the possibility to mix the standard chain complexes computing group cohomology and associative dialgebra cohomology. We also…