Transformations of Grassmannians and automorphisms of linear groups

The automorphism group of the quantum grassmannian

We calculate the automorphism group of the generic quantum grassmannian.

Fundamental Automorphisms of Clifford Algebras and an Extension of Dabrowski Pin Groups

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism between a finite group of the discrete transformations and an automorphism group of the Clifford algebras plays a central role. The complete classification of Dabrowski groups depending upon signatures of the spaces is given. Two types of Dabrowski quotient groups are introduced in case of odd-dimensional spaces. Application potentialities of the introduced q…

Noncommutative bispectral Darboux transformations

We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference operators with values in all noncommutative algebras. All known bispectral Darboux transformations are special cases of the theorem. Using the methods of quasideterminants and the spectral theory of matrix polynomials, we explicitly classify the set of bispectral Darboux transformations from rank one differential operators and Airy operators with values in matri…

n 维完全分次丝状李代数的局部和 2 - 局部自同构

Local and 2-Local automorphisms of n-dimensional totally graded filiform Lie algebras

研究最大长度的有限维完全分次复丝状李代数族的局部和 2 - 局部自同构空间，利用代数过滤等方法，通过分析多个序列和族，明确了不同结构中局部及 2 - 局部自同构的形式特点，划分出非线性与严格线性结构的边界。