I exhibit a pair of non-symmetric operads that, while not themselves isomorphic, induce isomorphic monads. The existence of such a pair implies that if ‘algebraic theory’ is understood as meaning ‘monad’ then operads cannot be regarded as algebraic theories of a special kind.

Let Q(α) and Q(β) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, Q(β) → Q(α). The algorithm is particularly efficient if there is only one isomorphism.

In this paper we prove a conjecture of B. Shoikhet. This conjecture states that the tangent isomorphism on homology, between the Poisson homology associated to a Poisson structure on R d and the Hochschild homology of its quantized star-product algebra , is an isomorphism of modules over the (isomorphic) respective cohomology algebras. As a consequence, we obtain a version of the Duflo isomorph...

Let G and K be groupoids. We present the notion of a (Gα,Kβ)-set we prove duality theorem in this context, which extends for graded algebras by groups. For A unital G-graded algebra X finite split G-set, show that there is an isomorphism between category X-graded left A-modules A#αGX-modules. As application isomorphism, construct Morita context.

We prove that, for a Poisson vertex algebra $${\cal V}$$ , the canonical injective homomorphism of variational cohomology to its classical is an isomorphism, provided that viewed as differential algebra, polynomials in finitely many variables. This theorem one key ingredients computation cohomology. For proof, we introduce sesquilinear Hochschild and Harrison complexes vanishing symmetric

We discuss the differential graded Lie algebra (DGLA) of Drinfeld modeled on the tensor algebra ⊗ Ug of the universal enveloping algebra of a Lie algebra g over any field K of characteristic zero. We explicitly analyze the first obstruction to the existence of the formality quasi-isomorphism for this DGLA. Our analysis implies the formality of the DGLA ⊗ Ub of Drinfeld associated to the twodime...

Classification theory guarantees the existence of an isomorphism between any two E8’s, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠ 2,3 an explicit isomorphism between the algebra obtained from J by Faulkner’s construction and the algebra obtained from the split ...

Then C∼(X) df = ⊕sC ∼(X) becomes a graded Q-algebra under the intersection product, and we define D∼(X) to be the Q-subalgebra of C∼(X) generated by the divisor classes: D∼(X) = Q[C ∼(X)]. The elements of D∼(X) will be called the Lefschetz classes on X (for the relation ∼). They are the algebraic classes on X expressible as linear combinations of intersections of divisor classes (including the ...

A non-standard quantum deformation of the two-photon algebra h6 is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock space and translated into Fock–Bargmann realizations that provide a direct formalism for the definition of deformed states of light. Finally, the isomorphism between h6 and the (1+1) Schrödinger algebra i...

We give an exposition of Novodvorskii’s theorem in Banach algebra K-theory, asserting that the Gelfand transform for a commutative induces isomorphism topological K-theory.