In this note we give examples of division rings which posses an anti-automorphism but no involution. The motivation for such examples comes from geometry. If D is a division ring and V a finite-dimensional right D-vector space of dimension ≥ 3, then the projective geometry P(V ) has a duality (resp. polarity) if and only if D has an anti-automorphism (resp. involution) [2, p. 97, p. 111]. Thus,...

We initiate the study of real $C^*$-algebras associated to higher-rank graphs $\Lambda$, with a focus on their $K$-theory. Following Kasparov and Evans, we identify spectral sequence which computes $\mathcal{CR}$ $K$-theory $C^*_{\mathbb R} (\Lambda, \gamma)$ for any involution $\gamma$ show that $E^2$ page this can be straightforwardly computed from combinatorial data $k$-graph $\Lambda$ $\gam...

Under the background of involution, impact peer effect on employee creativity provides ideas and directions for improvement enterprise innovation. Based this, this study explores influence moderating competitive atmosphere within organization in context involution. Research shows that under excessive regulates relationship between creativity, has a negative regulatory psychological safety; orga...

Using the concept of the λ-lattice introduced recently by V. Snášel we define λ-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.

Let G be a connected reductive algebraic group defined over an algebraically closed field F of characteristic not 2. Denote the Lie algebra of G by 9. In this paper we shall classify the isomorphism classes of ordered pairs of commuting involutorial automorphisms of G. This is shown to be independent of the characteristic of F and can be applied to describe all semisimple locally symmetric spac...

We present a solution to the problem of defining genus zero open Gromov–Witten invariants with boundary constraints for Lagrangian submanifold arbitrary dimension. Previously, such were known only in dimensions 2 and 3 from work Welschinger. Our approach does not require be fixed by an anti-symplectic involution, but can use if present, obtain stronger results. Also, non-trivial are defined bro...