On the Structure of Weyl-Type, Witt-Type, and Non-Associative Algebras over Expolynomial Rings

This paper introduces a generalized class of Weyl-type, Witt-type, and non-associative algebras constructed over an exponential–polynomial (expolynomial) framework. For fixed scalars ι1,…,ιr∈A and for fixed integers p=(p1,…,pn)∈Nn, we define the F-algebra Fe±xpeιx,eAx,xA, an expolynomial ring over a field F of characteristic zero, where A is an additive subgroup of F containing Z. This formulation extends the classical Weyl algebra through the integer power parameter p, which generates a family of non-isomorphic simple algebras. The corresponding Weyl-type algebra AFe±xpeιx,eAx,xA, the Witt-type Lie algebra WFe±xpeιx,eAx,xA, and their non-associative variants are examined in detail. The simplicity, grading, and automorphism structures of these algebras are established, and the dependence of these properties on the deformation parameter p is analyzed. All the constructed Weyl-type algebras, the corresponding Witt-type Lie algebras, and the non-associative algebras are shown to be simple under derivation structures. Many naturally occurring subalgebras, such as the integer-coefficient subalgebra AZe±xpeιx,eAx,xA, are also proven to be simple. Our analysis reveals that different choices of p result in non-isomorphic algebraic structures while retaining non-commutativity. The results obtained generalize several existing constructions of Weyl-type algebras and lay the theoretical foundation for further developments in transcendental and non-commutative algebraic frameworks.