5 citations · 15 across the 11 of their papers we have counts for
11 papers
Orthogonality graphs of real Cayley-Dickson algebras. Part I: Doubly alternative zero divisors and their hexagons
Svetlana Zhilina
We study zero divisors whose components alternate strongly pairwise and construct oriented hexagons in the zero divisor graph of an arbitrary real Cayley-Dickson algebra. In case o…
Orthogonality graphs of real Cayley-Dickson algebras. Part II: The subgraph on pairs of basis elements
Svetlana Zhilina
We consider zero divisors of an arbitrary real Cayley-Dickson algebra such that their components are both standard basis elements. We construct inductively the orthogonality graph…
Commuting graphs of Okubo algebras
Svetlana Zhilina, Danil Pavlinov
Commuting graphs of Okubo algebras are considered, and the problem of their connectivity is studied. The commuting graph of a pseudo-octonion algebra over a field…
Relation graphs of the sedenion algebra
Alexander Guterman, Svetlana Zhilina
Let denote the algebra of the sedenions, and denote its orthogonality graph. We observe that any pair of zero divisors in produces a dou…
On doubly alternative zero divisors in Cayley-Dickson algebras
Svetlana Zhilina
Zero divisors of Cayley-Dickson algebras over an arbitrary field , , are studied. It is shown that zero divisors, whose components a…
Diameter of the commutativity graph of the real sedenions
Svetlana Zhilina
The commutativity graph of the real sedenion algebra is considered. It is shown that those elements whose imaginary part is not a zero divisor correspond to isolated vertices of th…
Birkhoff-James classification of norm's properties
Alexander Guterman, Bojan Kuzma, Sushil Singla +1
For an arbitrary normed space over a field , we define the directed graph induced by Birkhoff-James orthogona…
On the lengths of Okubo algebras
Alexander Guterman, Svetlana Zhilina
We compute the lengths of two particular cases of (possibly non-unital) composition algebras, namely, standard composition algebras and Okubo algebras over an arbitrary field $\mat…
On the lengths of descendingly flexible and descendingly alternative algebras
Alexander Guterman, Svetlana Zhilina
We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field . We suggest a new method based on the sequence of diffe…
Roots and Critical Points of Polynomials over Cayley--Dickson Algebras
Adam Chapman, Alexander Guterman, Solomon Vishkautsan +1
We study the roots of polynomials over Cayley--Dickson algebras over an arbitrary field and of arbitrary dimension. For this purpose we generalize the concept of spherical roots fr…
What does Birkhoff-James orthogonality know about the norm?
Ljiljana Arambašić, Alexander Guterman, Bojan Kuzma +2
It is shown that Birkhoff-James orthogonality knows everything about the smooth norms in reflexive Banach spaces and can also compute the dimensions of the underlying normed spaces…