Related papers: Finite Groups of Essential Dimension 2
We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.
We describe structure of locally finite groups of finite centraliser dimension.
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
We summarize what is currently known about ed$(G)$ and RD$(G)$ for finite groups $G$ over $\mathbb{C}$ (i.e. in characteristic 0). In Appendix A, we also give an argument which improves the known bound on RD(PSL$(2,\mathbb{F}_{11})$).
The goal of this note is to reduce the existing upper bound for the essential dimension of central simple algebras of degree 8 and exponent 2 over fields of characteristic 2 from 10 to 9.
The maximal finite abelian subgroups, up to conjugation, of the simple algebraic group of type E8 over an algebraically closed field of characteristic 0 are computed. This is equivalent to the determination of the fine gradings on the…
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
We discuss essential dimension of group schemes, with particular attention to infinitesimal group schemes. We prove that the essential dimension of a group scheme of finite type over a field k is at least equal to the difference between the…
We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additionally, we classify the singularities of cluster algebras for…
We determine the fundamental group of period domains over finite fields.
Working over an arbitrary field, we define compact semisimple 2-categories, and show that every compact semisimple 2-category is equivalent to the 2-category of separable module 1-categories over a finite semisimple tensor 1-category. Then,…
By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…
In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is…
We study a family of finitely generated residually finite groups. These groups are doubles $F_2*_H F_2$ of a rank-$2$ free group $F_2$ along an infinitely generated subgroup $H$. Varying $H$ yields uncountably many groups up to isomorphism.
In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.
Let $F$ be a finite field of characteristic $p>0$ with $q = p^{n}$ elements. In this paper, a complete characterization of the unit groups $U(FG)$ of group algebras $FG$ for the abelian groups of order $32$, over finite field of…