Related papers: *-Jordan-type maps on alternative *-algebras
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
Let $A,B$ be C*-algebras, $B_A(0;r)$ the open ball in $A$ centered at $0$ with radius $r>0$, and $H:B_A(0;r)\to B$ an orthogonally additive holomorphic map. If $H$ is zero product preserving on positive elements in $B_A(0;r)$, we show, in…
A Jordan algebra J is said to be pseudo-euclidean if J is endowed with an associative non-degenerate symmetric bilinear form B. B is said an associative scalar product on J. First, we provide a description of the pseudo-euclidean Jordan…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…
We study an extension of the procedure to construct duality transformations among abelian gauge theories to the non abelian case using a path space formulation. We define a pre-dual functional in path space and introduce a particular non…
We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…
By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3 and the relation to the super-Ehlers symmetry in D = 5, we elucidate the massless multiplet structure of the spectrum of a broad class of D = 5 supergravity…
Nonassociative commutative algebras $A$ generated by idempotents $e$ whose adjoint operators ${\rm ad}_e\colon A \rightarrow A$, given by $x \mapsto xe$, are diagonalizable and have few eigenvalues are of recent interest. When certain…
An axial algebra over the field $\mathbb F$ is a commutative algebra generated by idempotents whose adjoint action has multiplicity-free minimal polynomial. For semisimple associative algebras this leads to sums of copies of $\mathbb F$.…
We characterise Exel's noncommutative Cartan subalgebras in several ways using uniqueness of conditional expectations, relative commutants, or purely outer inverse semigroup actions. We describe in which sense the crossed product…
We characterise when the Leavitt path algebras over $\mathbb{Z}$ of two arbitrary countable directed graphs are $*$-isomorphic by showing that two Leavitt path algebras over $\mathbb{Z}$ are $*$-isomorphic if and only if the corresponding…
In the present work, we study Yetter-Drinfeld algebras over a pairing of multiplier Hopf algebras. Our main motivation is the construction of a self-dual theory of (C*-)algebraic quantum transformation groupoids. Instead of the standard…
The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field of characteristic not 2. We obtained a list of 35 isolated non-isomorphic 5-dimensional nilpotent non-associative Jordan…
For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…
This is the second of a series of papers which aim towards a classification of edge-transitive maps of which the Euler characteristic and the edge number are coprime. This one carries out the classification work for arc-transitive maps with…
We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products.
In the present paper we introduce and investigate the notion of 2-local linear map on vector spaces. A sufficient condition is obtained for linearity of a 2-local linear map on finite dimensional vector spaces. Based on this result we prove…
Let $\mathcal{A}$ and $\mathcal{B}$ be two factor von Neumann algebras and $\eta$ be a non-zero complex number. A nonlinear bijective map $\phi:\mathcal A\rightarrow\mathcal B$ has been demonstrated to satisfy…
Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities $a(bc) = a(cb)$, $(ba)a^2 = (ba^2)a$, and $(b,a^2,c) = 2(b,a,c)a$. These identities are satisfied by the product $ab = a \dashv b + b…
In the study of pre-Lie algebras, the concept of pre-morphism arises naturally as a generalization of the standard notion of morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative…