Related papers: On the isomorphism problem for central extensions …

Non-Abelian duality transformations built on non-semi-simple isometry groups are analysed. We first give the conditions under which the original non-linear sigma model and its non-Abelian dual are equivalent. The existence of an invariant…

This is one of a series papers which aim towards to solve the problem of determining automorphism groups of Frobenius groups. This one solves the problem in the case where the Frobenius kernels are elementary abelian and Frobenius…

For which finite subgroups G of SL(r,C), r \geq 4, are there crepant desingularizations of the quotient space C^r/G? A complete answer to this question (also known as "Existence Problem" for such desingularizations) would classify all those…

If A and B are abelian varieties over a number field K such that there are non-trivial geometric homomorphisms of abelian varieties between reductions of A and B at most primes of K, then there exists a non-trivial (geometric) homomorphism…

We consider 9 infinite families of finite $p$-groups, for $p$ a prime, and we settle the isomorphism problem that arises when the parameters that define these groups are modified.

We show that any Kahler extension of a finitely generated abelian group by a surface group of genus g at least 2 is virtually a product. Conversely, we prove that any homomorphism of an even rank, finitely generated abelian group into the…

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra…

The central extension of the Thompson group $T$ that arises in the quantized Teichm\"uller theory is 12 times the Euler class. This extension is obtained by taking a (partial) abelianization of the so-called braided Ptolemy-Thompson group…

Cosetal extensions of monoids generalise extensions of groups, special Schreier extensions of monoids and Leech's normal extensions of groups by monoids. They share a number of properties with group extensions, including a notion of Baer…

Let X=G/H be the quotient of a connected reductive algebraic C-group G defined over the field of complex numbers C by a finite subgroup H. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when H…

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…

Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of…

We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…

This paper suveys some recent algebraic developments in two parameter Quantum deformations and their Nonstandard (or Jordanian) counterparts. In particular, we discuss the contraction procedure and the quantum group homomorphisms associated…

In a previous joint paper with Wu and Yakimov, we gave an explicit description of the lowest discriminant ideal in Cayley-Hamilton Hopf algebras $(H,C,\mathrm{tr})$ with basic identity fiber, i.e. all irreducible representations over the…

We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.

In this paper we describe a family of isomorphism invariants of a finitely generated Coxeter group W. Each of these invariants is the isomorphism type of a quotient group W/N of W by a characteristic subgroup N. The virtue of these…

We continue the study of the lower central series L_i(A) and its successive quotients B_i(A) of a noncommutative associative algebra A, defined by L_1(A)=A, L_{i+1}(A)=[A,L_i(A)], and B_i(A)=L_i(A)/L_{i+1}(A). We describe B_{2}(A) for A a…

We show that elementary abelian direct factors can be disregarded in the study of the modular isomorphism problem. Moreover, we obtain four new series of abelian invariants of the group base in the modular group algebra of a finite…

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian…