We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. characterize homomorphism posets of finite algebras terms disjoint unions dual partition lattices and investigate reconstruction problems homomorphisms.

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra [1],[3],[13]. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra [13]. We also generalize the Hamitonian Lie algebra using exponential functions, and we show that these Lie algebras are simple.

We study algebraic neural networks (AlgNNs) with commutative algebras which unify diverse architectures such as Euclidean convolutional networks, graph and group under the umbrella of signal processing. An AlgNN is a stacked layered information processing structure where each layer conformed by an algebra, vector space homomorphism between algebra endomorphisms space. Signals are modeled elemen...

We consider the double affine Hecke algebra H = H(k0, k1, k∨ 0 , k ∨ 1 ; q) associated with the root system (C∨ 1 , C1). We display three elements x, y, z in H that satisfy essentially the Z3-symmetric Askey–Wilson relations. We obtain the relations as follows. We work with an algebra Ĥ that is more general than H, called the universal double affine Hecke algebra of type (C∨ 1 , C1). An advanta...

In this paper, some properties of the dual B-homomorphism are provided, along with natural and fundamental theorem B-homomorphisms for B-algebras. The first third isomorphism theorems B algebra also presented in paper.

We define type A, type B, type C as well as C∗-semi-finite C∗-algebras. It is shown that a von Neumann algebra is a type A, type B, type C or C∗-semi-finite C∗-algebra if and only if it is, respectively, a type I, type II, type III or semi-finite von Neumann algebra. Moreover, any type I C∗-algebra is of type A (actually, type A coincides with the discreteness as defined by Peligrad and Zsidó),...

In this paper we discuss a relationship between the following two algebras: (i) the subconstituent algebra T of a distance-regular graph that has q-Racah type; (ii) the q-tetrahedron algebra ⊠q which is a q-deformation of the three-point sl2 loop algebra. Assuming that every irreducible T -module is thin, we display an algebra homomorphism from ⊠q into T and show that T is generated by the imag...

We consider a simple solution of a Yang-Baxter equation on loop algebra and deduce from it a Sklyanin Poisson structure which operates continuously on a Sobolev test algebra on the Wiener space of the Lie algebra. It is very classical that the solution of the classical Yang-Baxter equation on a finite dimensional algebra gives a Poisson structure on the algebra of smooth function on the finite ...

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...