A set of valuable universal similarity factorization equalities are established over complex Clifford algebras Cn. Through them matrix representations of complex Clifford algebras Cn can directly be derived, and their properties can easily be determined. AMS Subject Classification: 15A23, 15A66.

The abstract representation-free Algebra of the past century is unable to formalize algebra sameness. A counterexample shows a universal transformation that cannot be representation-free. Then, to define transformations between based universal algebras we must introduce the representations corresponding to the bases, contrary to what was possible in general vector spaces and believed possible i...

We provide a construction, refined from an inverse limit, that produces the mod 2 Steenrod and Dyer-Lashof algebras from each other. In fact, the construction relates various subalgebras and quotients of the universal Steenrod algebra of operations for H∞-ring spectra. We also describe how the construction transforms the axiomatic properties of homogeneous pre-Koszul algebras and Poincaré-Birkh...

Codescent morphisms are described in regular categories which satisfy the so-called strong amalgamation property. Among varieties of universal algebras possessing this property are, as is known, categories of groups, not necessarily associative rings, M -sets (for a monoid M), Lie algebras (over a field), quasi-groups, commutative quasi-groups, Steiner quasi-groups, medial quasigroups, semilatt...

Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal C∗-algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph C∗-algebras to study the K-theory and gauge-invariant ideal structure of ultragraph C∗-al...

Introduction 2 1. Lie algebras: recollections 3 1.1. The basics 3 1.2. Scaling the structure 3 1.3. Filtrations 4 1.4. The Chevalley complex 4 1.5. The functor of primitives 6 1.6. The enhanced adjunction 6 1.7. The symmetric Hopf algebra 8 2. Looping Lie algebras 9 2.1. Group-Lie algebras 10 2.2. Forgetting to group structure 10 2.3. Chevalley complex of group-Lie algebras 11 2.4. Chevalley co...

In algebraic geometry over a variety of universal algebras Θ, the group Aut(Θ) of automorphisms of the category Θ of finitely generated free algebras of Θ is of great importance. In this paper, we prove that all automorphisms of categories of free S-acts are semi-inner, which solves a variation of Problem 12 in [12] for monoids. We also give a description of automorphisms of categories of finit...

Let /C be a class of (universal) algebras of fixed type. /C* denotes the class obtained by augmenting each member of K, by the ternary discriminator function (/(x,y, z) = x if x / ?/, ^(x,x,z) = 2:), while V(/C*) is the closure of /C* under the formation of subalgebras, homomorphic images, and arbitrary Cartesian products. For example, the class of Boolean algebras is definitionally equivalent ...

The paper is essentially a continuation of [PZ], whose main notion is that of logic-geometrical equivalence of algebras (LG-equivalence of algebras). This equivalence of algebras is stronger than elementary equivalence. In the paper we introduce the notion of isotyped algebras and relate it to LG-equivalence. We show that these notions coincide. The idea of the type is one of the central ideas ...

We introduce the concept of pseudotwistor (with particular cases called twistor and braided twistor) for an algebra (A,μ, u) in a monoidal category, as a morphism T : A⊗ A → A ⊗ A satisfying a list of axioms ensuring that (A,μ ◦ T, u) is also an algebra in the category. This concept provides a unifying framework for various deformed (or twisted) algebras from the literature, such as twisted ten...