The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent com...

Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between graphs classical graphs. This is naturally cast as “quantum–classical game,” that is, of two players involving questions answers. generalizes the We show winning strategies in various models for an analog notion non-commutative homomorphisms due to Stahlke [IEEE Trans. Inf. Theory 62(1), 5...

Abstract We prove results for the study of double copy and tree-level colour/kinematics duality scattering amplitudes using properties Lie polynomials. show that ‘ S -map’ was defined to simplify super-Yang–Mills multiparticle superfields is in fact a bracket. A generalized KLT map from polynomials their dual obtained by studying our new bracket; matrix elements this yield recently proposed ‘ge...

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

In [1],the authors defined algebra homomorphisms from the dual RingelHall algebra of certain hereditary abelian categoryA to an appropriate q-polynomial algebra. In the case that A is the representation category of an acyclic quiver, we give an alternative proof by using the cluster multiplication formulas in [9]. Moreover, if the underlying graph of Q is bipartite and the matrix B associated t...

An explicit description of free strongly homotopy associative and free strongly homotopy Lie algebras is given. A variant of the Poincaré-Birkhoff-Witt theorem for the universal enveloping A(m)-algebra of a strongly homotopy Lie algebra is formulated. Introduction This note was originated many years ago as my reaction to questions of several people how free strongly homotopy algebras can be des...