Related papers: Linear representation of Abel-Grassmann groups
In this paper we study a relationship between elementary equivalence of endomorphism rings of Abelian p-groups and second order equivalence of the corresponding Abelian p-groups.
We provide an algebraic characterization of strong ordered Abelian groups: An ordered Abelian group is strong iff it has bounded regular rank and almost finite dimension. Moreover, we show that any strong ordered Abelian group has finite…
Let G be a connected reductive algebraic group over a perfect field. We study the representability of the equivariant automorphism group of G-varieties. For a broad class of complexity-one G-varieties, we show that this group is…
In this paper we extend a result for representations of the Additive group $G_a$ given in [3] to the Heisenberg group $H_1$. Namely, if $p$ is greater than 2d then all $d$-dimensional characteristic $p$ representations for $H_1$ can be…
Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have…
A global representation is a compatible collection of representations of the outer automorphism groups of the finite groups belonging to a family $\mathscr{U}$. These arise in classical representation theory, in the study of representation…
We prove that non-trivial representations of the alternating group $A_n$ are reducible over a primitive proper subgroup which is isomorphic to some alternating group $A_m$.
We enumerate the number of complex irreducible representations of each degree of general unitary groups of degree 4 over principal ideal rings of length 2.
We study a family of complex representations of the group GL(n,O), where O is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL(n,F) to its maximal…
We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.
In this paper we prove an Ax-Schanuel type result for the exponential functions for general linear groups over $\mathbb{C}$. We prove the result first for the group of upper triangular matrices and then for the group $GL_n$ of all $n\times…
We use the endoscopic classification of automorphic representations of even-dimensional unitary groups to construct level-raising congruences.
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.
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of…
We give the classification of all possible G-graphs for any small binary dihedral subgroup G in GL(2,C) and use this classification to give the combinatorial description of the special representations of G in terms of its maximal cyclic…
We give an introductory account of Khovanov's categorification of the Heisenberg algebra, and construct a combinatorial model for it in a 2-category of spans of groupoids. We also treat a categorification of $U(sl_n)$ in a similar way.…
Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the…
We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie…
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants…
In this paper, we give a new series of coboundary operators of Hom-Lie algebras. And prove that cohomology groups with respect to coboundary operators are isomorphic. Then, we revisit representations of Hom-Lie algebras, and generalize the…