The relation $$xy-yx=h(y)$$ , where $$h$$ is a holomorphic function, occurs naturally in the definitions of some quantum groups. To attach rigorous meaning to right-hand side this equality, we assume that $$x$$ and $$y$$ are elements Banach algebra (or an Arens–Michael algebra). We prove universal generated by commutation kind can be represented explicitly as analytic Ore extension. An analysis...

Order-sorted algebras and many sorted algebras exist in a long history with many different implementations and applications. A lot of language specifications have been defined in order-sorted algebra frameworks such as the language specifications in K (an order-sorted algebra framework). The biggest problem in a lot of the order-sorted algebra frameworks is that even if they might allow develop...

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for chec...

The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra. Classical results of Kostant [7] give a fairly complete invarianttheoretic picture of the (co)adjoint representation of g. Let σ ∈ Aut(g) be an involution and g = g0 ⊕ g1 the corresponding Z2-grading. Associated to this decomposition, there is a non-reductive Lie algebra k = g0 ⋉ g...

The number of distinct operations (that is, the range of the variable a) may be infinite, but for our main result (Theorem 2), we shall require every n(a) to be finite—that is, it will concern algebras with finitary operations. The concepts of subalgebra, congruence relation on an algebra, homomorphism of one algebra A onto (or into) another algebra with the same operations, and of the direct u...

We investigate algorithms for solving the satisfiability problem in composition-nominative logics of quantifier-equational level. These logics are algebra-based logics of partial predicates constructed in a semantic-syntactic style on the methodological basis, which is common with programming; they can be considered as generalizations of traditional logics on classes of partial predicates that ...

A translation technique is presented which transforms a class of First Order Logic formulas, called Restricted formulas, into ground formulas. For the formulas in this class the range of quanti ed variables is restricted by Domain formulas. If we have a complete knowledge of the predicates involved in the Domain formulas their extensions can be evaluated with the Relational Algebra and these ex...

We show how to write generic programs and proofs in MartinLöf type theory. To this end we consider several extensions of MartinLöf’s logical framework for dependent types. Each extension has a universes of codes (signatures) for inductively defined sets with generic formation, introduction, elimination, and equality rules. These extensions are modeled on Dybjer and Setzer’s finitely axiomatized...

We introduce a new abstract domain, namely the domain of Interval Linear Equalities (itvLinEqs), which generalizes the affine equality domain with interval coefficients by leveraging results from interval linear algebra. The representation of itvLinEqs is based on a row echelon system of interval linear equalities, which natively allows expressing classical linear relations as well as certain t...