Related papers: Clifford Algebras and Graphs
We introduce a notion of ideal-related K-theory for rings, and use it to prove that if two complex Leavitt path algebras are Morita equivalent (respectively, isomorphic), then the ideal-related K-theories (respectively, the unital…
We give a precise description of combed trees in terms of Kelly-Mac Lane graphs. We show that any combed tree is uniquely expressed as an allowable Kelly-Mac Lane graph of a certain shape. Conversely, we show that any such Kelly-Mac Lane…
We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the $\textit{Clifford group}$, a subgroup inside the Clifford algebra…
A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to…
In the present paper, we determine the group of automorphisms of pseudo $H$-type Lie algebras, which are two-step nilpotent Lie algebras closely related to the Clifford algebras $\Cl(\mathbb R^{r,s})$.
The aim of this work is the description of the isomorphism classes of all Leavitt path algebras coming from graphs satisfying Condition (Sing) with up to three vertices. In particular, this classification recovers the one achieved by Abrams…
Algebras associated with Quantum Electrodynamics and other gauge theories share some mathematical features with T-duality Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be…
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold ($C$-space) consists not…
Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford…
An Adinkra is a graph from the study of supersymmetry in particle physics, but it can be adapted to study Clifford algebra representations. The graph in this context is called a Cliffordinkra, and puts some standard ideas in Clifford…
The Lie algebraic integrability test is applied to the problem of classification of integrable Klein-Gordon type equations on quad-graphs. The list of equations passing the test is presented containing several well-known integrable models.…
This survey purports to be an elementary introduction to compactly presented groups, which are the analogue of finitely presented groups in the broader realm of locally compact groups. In particular, compact presentation is interpreted as a…
An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones.…
In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…
We introduce the notion of a topological higher-rank graph, a unified generalization of the higher-rank graph and the topological graph. Using groupoid techniques, we define the Toeplitz and Cuntz-Krieger algebras of topological higher-rank…
For any countable graph $E$, we investigate the relationship between the Leavitt path algebra $L_{\C}(E)$ and the graph C*-algebra $C^*(E)$. For graphs $E$ and $F$, we examine ring homomorphisms, ring *-homomorphisms, algebra homomorphisms,…
Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…
Kaplansky introduced the notions of CCR and GCR $C^*$-algebras because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this paper we characterize when the algebra of an ample…
A set of valuable universal similarity factorization equalities is established over complex Clifford algebras $\Cn.$ Through them matrix representations of complex Clifford algebras $\Cn$ can directly be derived, and their properties can…
We describe derivations of the Clifford algebra of a nondegenerate quadratic form on a countable dimensional vector space over an algebraically closed field of characteristic not equal to $2$. We also construct an algebraic automorphism of…