A bstract We study compactifications on AdS 3 × S and deformations thereof. exploit the triality symmetry of underlying duality group SO(4,4) three-dimensional supergravity in order to construct relate new consistent truncations. For non-chiral D = 6, $$ \mathcal{N} N 6d (1 , 1) supergravity, we find two diff...

This article consists of three parts that are largely independent of one another. The first part deals with the projective geometry of homogeneous varieties, in particular their secant and tangential varieties. It culminates with an elementary construction of the compact Hermitian symmetric spaces and the closed orbits in the projectivization of the adjoint representation of a simple Lie algebr...

We describe all the fine group gradings, up to equivalence, on the Lie algebra d4. This problem is equivalent to finding the maximal abelian diagonalizable subgroups of the automorphism group of d4. We prove that there are fourteen by using two different viewpoints. The first approach is computational: we get a full description of the gradings by using a particular implementation of the automor...

We experimentally verify the link existing between entanglement and amount of wave-particle duality in a bipartite quantum system, with superconducting qubits IBM Q computer. consider both pure mixed states, study influence state purity on observation complementarity "triality" relation Jakob Bergou. This work confirms quantitative completion local Bohr's principle by nonlocal typical truly sys...

We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over commutative semiring S. In particular, we obtain complete characterization congruence-simpleness for such Steinberg algebras, extending well-known characterizations when S is field or ring. also provide criterion AS(GE) graph groupoid GE associated to an arbitrary E be congruence-simple. Motivated result Cla...

This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based the author's memoir arXiv:0905.2621. The paper intended to serve as pedagogical introduction and summary of covariant between DG-algebras curved DG-coalgebras, well triality DG-modules, CDG-comodules, CDG-contramodules. Some personal reminiscences are included part historical discussion.

Let G be a reductive connected algebraic group over an algebraic closure of a finite field of characteristic p. Let F be a Frobenius endomorphism on G and write G := G F for the corresponding finite group of Lie type. We consider projective characters of G in characteristic p of the form St ·β, where β is an irreducible Brauer character and St the Steinberg character of G. Let M be a rational G...