Related papers: Eigentheory of Cayley-Dickson algebras

We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizations of this kind and yields a way to obtain more tilted…

We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.

We consider the family of undirected Cayley graphs associated with odd cyclic groups, and study statistics for the eigenvalues in their spectra. Our results are motivated by analogies between arithmetic geometry and graph theory.

The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable sequences is a Cayley-Dickson algebra.

We introduce the notion of eigenstate of an operator in an abstract C*-algebra, and prove several properties. Most significantly, if the operator is self-adjoint, then every element of its spectrum has a corresponding eigenstate.

An algebraic deformation theory of dialgebra morphisms is obtained.

It is determined exactly which classifiable C*-algebras have approximately inner flip. The answer includes a number of C*-algebras with torsion in their K-theory, and a number of C*-algebras that are self-absorbing but not strongly…

In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…

The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.

Algebraic $K$-theory is a homology theory that behaves very well on sufficiently nice objects such as stable $C^*$-algebras or smooth algebraic varieties, and very badly in singular situations. This survey explains how to exploit this to…

This work is concerned with the notion of {eigenstates} for $C^*$-algebras. After reviewing some basic and structural results, we explore the possibility of reinterpreting certain typical concepts of quantum mechanics (\eg dynamical…

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.

The Cayley-Dickson algebra has long been a challenge due to the lack of an explicit multiplication table. Despite being constructible through inductive construction, its explicit structure has remained elusive until now. In this article, we…

we study the exponential map for A_n = R^2^n, the Cayley_Dickson algebras for n bigher than 1,wich generalize the Complex exponential map to Quaternions,Octonions and so forth. As application,we show that the self-map of the unit sphere in…

The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.

We work to find a basis of graded identities for the octonion algebra. We do so for the $\mathbb{Z}_2^2$ and $\mathbb{Z}_2^3$ gradings, both of them derived of the Cayley-Dickson process, the later grading being possible only when the…

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…

Algebraic K-theory is the stable homotopy theory of homotopy theories, and it interacts with algebraic structures accordingly. In particular, we prove the Deligne Conjecture for algebraic K-theory.

We introduce and study elementary properties of graph homology of algebras. This new homology theory shares many features of cyclic and Hochschild homology. We also define a graph K-theory together with an analog of Chern character.