Related papers: Idempotent geometry in generic algebras

Let $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent…

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles…

This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…

A Lie 2-algebra is a "categorified" version of a Lie algebra: that is, a category equipped with structures analogous those of a Lie algebra, for which the usual laws hold up to isomorphism. In the classical mechanics of point particles, the…

Deformed $\mathfrak{g}_2$ exceptional applications are introduced via the Clifford algebra-parametrized formalism. Using the products between multivectors of $\cl_{0,7}$, the Clifford algebra over the metric vector space $\RR^{0,7}$, and…

In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by {\it Clifford cohomology.} We show that {\it Clifford…

The notions of idempotental identities and axial identities of axial algebras are introduced, in order to understand better some theorems of J.~Desmet, I.~Gorshkov, S.~Shpectorov, and A.~Staroletov about solid subalgebras; this approach…

Let A and A' be two alternative *-algebras with identities 1_A and 1_A', respectively, and e_1 and e_2 = 1_A - e_1 nontrivial symmetric idempotents in A. In this paper we study the characterization of multiplicative *-Jordan-type maps on…

Let $\mathcal{J}$ be the exceptional Jordan algebra and $V=\mathcal{J}\oplus \mathcal{J}$. We construct an equivariant map from $V$ to $\mathrm{Hom}_k(\mathcal{J}\otimes \mathcal{J},\mathcal{J})$ defined by homogeneous polynomials of degree…

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…

Binary idempotent semirings govern classical path algebras. Their multiplicative structure is dyadic. We examine whether this restriction is structural or accidental. We define ternary idempotent $\Gamma$-semirings as higher-arity ordered…

A generalization of the term "generalized Clifford algebras" (as appears in papers on advances in applied Clifford algebras) is introduced. This algebra is studied by means of structure theory of central simple algebras. A graph theoretical…

Consider two non-degenerate algebras B and C over the complex numbers. We study a certain class of idempotent elements E in the multiplier algebra of the tensor product of B with C, called separability idempotents. The conditions include…

We study the representation theoretic results of the binary cubic generic Clifford algebra $\mathcal C$, which is an Artin-Schelter regular algebra of global dimension five. In particular, we show that $\mathcal C$ is a PI algebra of PI…

We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many…

We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further.

Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…

Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real…