Related papers: Condensation and left-orderable groups
We solve the twisted conjugacy problem on Thompson's group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut_+(F) are orbit decidable provided a certain conjecture on Thompson's group T is true.…
We show that the Baumslag-Solitar group $BS(1,2)$ is undistorted in the Lodha-Moore group $G_0$ using an explicit lower bound for the word length of $G_0$. We also show that Thompson's group $F$ is distorted in $G_0$.
A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…
We construct non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and other left distributive systems. Instantiations of these protocols using generalized shifted conjugacy in braid groups lead to…
We generalize a result of T. Koberda by showing that the natural action of the automorphism group on the space of left-orderings is faithful for all nonabelian bi-orderable groups G, as well as for a certain class of left-orderable groups…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
We apply a new bosonization technique to relativistic field theories of fermions whose partition function is dominated by bosonic composites, and derive the effective action for these bosons. The derivation respects all symmetries,…
The Baumslag-Solitar groups and their certain variations are a-T-menable. This is proved by embeding them into topological groups and studying representation theoretic properties of the latter. The paper is motivated by the questions of A.…
Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…
In a group $G$, elements $a$ and $b$ are conjugate if there exists $g\in G$ such that $g^{-1} ag=b$. This conjugacy relation, which plays an important role in group theory, can be extended in a natural way to inverse semigroups: for…
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
We study the homology of pointed sets over a partially commutative monoid.
We discuss the question whether left-orderable groups satisfying a nontrivial law are locally indicable.
This paper is centred on solving differential equations by symmetry groups for first order ODEs and is in response to Starrett (2007). It also explores the possibility of averting the assumptions by Olver (2000) that, in practice finding…
We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…
We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed…
For a group $G$, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.
Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…
We prove that an HNN extension of a torsion-free nilpotent group is left-orderable. We also construct examples of non-left-orderable HNN extensions of left-orderable groups
We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current…