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We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra…

Algebraic Topology · Mathematics 2016-01-27 Fernando Muro

We describe a type of Lie color algebra, which we call generic, whose universal enveloping algebra is a domain with finite global dimension. Moreover, it is an iterated Ore extension. We provide an application and show Grobner basis methods…

Representation Theory · Mathematics 2007-05-23 Kenneth L. Price

The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with…

Mathematical Physics · Physics 2009-07-22 Angel Ballesteros , Alfonso Blasco , Francisco J. Herranz , Fabio Musso , Orlando Ragnisco

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…

Algebraic Topology · Mathematics 2016-01-20 Alexander Berglund

A. L. Agore and G. Militaru constructed a new invariant (a ``universal coacting Hopf algebra") for some finite-dimensional binary quadratic algebras such as Lie/Leibniz algebras, associative algebras, and Poisson algebras with prominent…

Rings and Algebras · Mathematics 2025-07-09 Saikat Goswami , Satyendra Kumar Mishra , Suman Pattanayak

We use Arkhipov's twisting functors to show that the universal enveloping algebra of a semi-simple complex finite-dimensional Lie algebra surjects onto the space of ad-finite endomorphisms of the simple highest weight module $L(\lambda)$,…

Representation Theory · Mathematics 2010-04-02 Volodymyr Mazorchuk

Let $(S,L)$ be a Lie-Rinehart pair such that $L$ is $S$-projective and let $U$ be its universal enveloping algebra. The purpose of this paper is to present a spectral sequence which converges to the Hochschild cohomology of $U$ and whose…

K-Theory and Homology · Mathematics 2020-06-05 Francisco Kordon

Explicit constructions for the minimal models of general and unimodular L-infinity algebra structures are given using the BV-formalism of mathematical physics and the perturbative expansions of integrals. In particular, the general formulas…

Quantum Algebra · Mathematics 2024-08-23 James Maunder

This article explores \Z_2-graded L_\infinity algebra structures on a 2|1-dimensional vector space. The reader should note that our convention on the parities is the opposite of the usual one, because we define our structures on the…

Quantum Algebra · Mathematics 2007-05-23 Derek Bodin , Alice Fialowski , Michael Penkava

We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C*-algebra to the C*-algebra generated by any other contraction. A universal contraction may be irreducible or a direct sum of…

Operator Algebras · Mathematics 2019-05-06 Kristin Courtney , David Sherman

Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ algebra via the homological…

Mathematical Physics · Physics 2023-07-31 Martin Doubek , Branislav Jurčo , Ján Pulmann

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal…

Differential Geometry · Mathematics 2007-05-23 D. Iglesias , J. C. Marrero

We propose a sequential topology on the space of sub-$\sigma$-algebras of a separable probability space $(\Omega,\mathcal{F},\mathbb{P})$ by linking conditional expectations on $L^{2}$ along sequences of sub-$\sigma$-algebras. The varying…

Probability · Mathematics 2021-05-20 Patrick Beissner , Jonas M. Tölle

We propose a new definition of so called Hamiltonian forms in n-plectic geometry and show that they have a non-trivial Lie infinity-algebra structure.

Differential Geometry · Mathematics 2012-12-21 Mirco Richter

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

Representation Theory · Mathematics 2012-10-23 Marcus J. Slupinski , Robert J. Stanton

We give a systematic construction of the symmetries, or observables in the vacuum sector, of a full conformal field theory on an arbitrary real two-dimensional conformal manifold $\Sigma$. Specifically, we construct a prefactorisation…

High Energy Physics - Theory · Physics 2025-12-08 Benoit Vicedo

Let L be a p-adic local field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) is a stably flat completion of its universal enveloping algebra. As a consequence the relative cohomology for the…

Representation Theory · Mathematics 2012-12-17 Tobias Schmidt

We introduce a new class of infinite-dimensional Lie algebras, which we refer to as continuum Kac-Moody algebras. Their construction is closely related to that of usual Kac-Moody algebras, but they feature a continuum root system with no…

Representation Theory · Mathematics 2022-07-19 Andrea Appel , Francesco Sala , Olivier Schiffmann

We compute reduced Hochschild cohomology of B = Ext\star (O \oplus L, O \oplus L), where O is the structure sheaf of an elliptic curve and L is a line bundle of degree 1. The result suggests an A-infinity equivalence between the A-infinity…

Algebraic Geometry · Mathematics 2011-11-29 Robert Fisette

We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional algebras, the nilpotency condition is necessary for a…

Rings and Algebras · Mathematics 2024-12-31 H. Alhussein , P. Kolesnikov