Related papers: Non-arithmetic lattices and the Klein quartic
We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for a Poisson algebra. Introduce and investigate noncommutative…
We consider the automorphism groups of various Lorentzian lattices over the Eisenstein, Gaussian, and Hurwitz integers, and in some of them we find reflection groups of finite index. These provide new finite-covolume reflection groups…
In "Non arithmetic super rigid groups: counter examples to Platonov's conjecture" Bass and Lubotzky gave a counter example to Platonov's conjecture by presenting an example of a linear group with super-rigidity which is not an arithmetic…
We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg…
We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single…
We construct the quartic version of generalized quasi-topological gravity, which was recently constructed to cubic order in arXiv: 1703.01631. This class of theories includes Lovelock gravity and a known form of quartic quasi-topological…
In this article we characterize the extreme points of the unit ball of a non-commutative (quantum) Lorentz space associated with a semi-finite von Neumann algebra. This enables us to show that surjective isometries between non-commutative…
Following [Botur, M., Chajda, I., Hala\v{s}, R.: Are basic algebras residuated structures?, Soft Comput. 14 (2010), 251-255] we discuss the connections between left-residuated partially ordered groupoids and the so-called basic algebras,…
We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space $D=SU(m,1)/U(m)$, with the method of coherent state quantization. In the commutative limit we obtain the standard…
In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…
We present a scheme of biquaternionic algebrodymamics based on a nonlinear generalization of the Cauchy-Riemann holomorphy conditions considered therein as fundamental field equations. The automorphism group SO(3,C) of the biquaternion…
We explore the differential geometry of finite sets where the differential structure is given by a quiver rather than as more usual by a graph. In the finite group case we show that the data for such a differential calculus is described by…
This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$--orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a…
In an earlier paper by three of the present authors and Csaba Schneider, it was shown that, for $m\ge2$, a set of $m+1$ partitions of a set $\Omega$, any $m$ of which are the minimal non-trivial elements of a Cartesian lattice, either form…
Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…
We apply G. Prasad's volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of SO(1,n). As a result we prove that for any even dimension n there exists a…
We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…
Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a…
Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations…
We describe a general procedure to produce fundamental domains for complex hyperbolic triangle groups, a class of groups that contains a representative of the commensurability class of every known non-arithmetic lattice in ${\rm PU}(2,1)$.…