A bstract L ∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze Gauged Double Field Theory in generalized flux formalism. The symmetry transformations consist a deformed Lie derivative and double Lorentz transformations. We obtain all non-trivial products closed form considering Kerr-Schild ansatz for frame include linear p...

The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series H = ln(ee ) for noncommuting X, Y . Formally H lives in the graded completion of the free Lie algebra L generated by X, Y . We present a closed explicit formula for H = ln(ee ) in a linear basis of the graded completion of the free metabelian Lie algebra L̄ = L/[[L, L], [L, L]].

Introduction. In theory, the bar construction suffices to calculate the homology groups of an augmented algebra. In practice, the bar construction is generally too large (has too many generators) to allow computation of higher-dimensional homology groups. In this paper, we outline a procedure which simplifies the calculation of the homology and cohomology of Hopf algebras. Let i b e a (graded) ...

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

It is shown that any simple, rational and C2-cofinite vertex operator algebra whose weight 1 subspace is zero, the dimension of weight 2 subspace is greater than or equal to 2 and with central charge c = 1, is isomorphic to L(12 , 0) ⊗ L( 1 2 , 0). 2000MSC:17B69

We consider the algebra $\dot\Sigma(\mathcal L)$ generated by inner-limit derivations over ${\rm GICAR}$ of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to lattice, we demonstrate that image $\dot \Sigma(\mathcal through Fock representation can be completed gro...

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Let K/Q be a finite Galois extension with the Galois group G, and let χ be a nontrivial irreducible character ofG. Artin’s conjecture predicts that the L-function L(s, χ,K/Q) is holomorphic in the whole complex plane ([1], P. 105). Let χ1, . . . , χr be the irreducible nontrivial characters of G. The corresponding L-functions L(s, χ1), . . . , L(s, χr) are algebraically independent over C ([2],...