16 citations · 36 across the 14 of their papers we have counts for
15 papers
Invertible Morava motives in quadrics
Andrei Lavrenov, Pavel Sechin
We associate to any element in the Milnor K-theory of a field modulo 2 an invertible Morava K-theory motive over . Specifically, for in $\mathrm{K}^{\mathrm{M}}_{n+1}(k)…
Morava -invariant
Nikita Geldhauser, Andrei Lavrenov, Victor Petrov +1
We compute the co-multiplication of the algebraic Morava K-theory for split orthogonal groups. This allows us to compute the decomposition of the Morava motives of generic maximal…
Bounded generation of Steinberg groups over Dedekind rings of arithmetic type
Boris Kunyavskii, Andrei Lavrenov, Eugene Plotkin +1
The main result of the present paper is bounded elementary generation of the Steinberg groups for simply laced root systems of rank and arbitrary Ded…
Morava K-theory and Rost invariant
Andrei Lavrenov, Victor Petrov
We prove that inner forms of a variety of Borel subgroups have isomorphic motives with respect to the second Morava K-theory if and only if the corresponding Tits algebras and Rost…
On the -invariance of modeled on linear and even orthogonal groups
Andrei Lavrenov, Sergey Sinchuk, Egor Voronetsky
Let be an arbitrary field. In this paper we show that in the linear case (, ) and even orthogonal case (, , $\ma…
Morava K-theory of orthogonal groups and motives of projective quadrics
Nikita Geldhauser, Andrei Lavrenov, Victor Petrov +1
We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of spec…
Centrality of for Chevalley groups: a pro-group approach
Andrei Lavrenov, Sergey Sinchuk, Egor Voronetsky
We prove the centrality of for an arbitrary commutative ring . This completes the proof of the centrality of for any roo…
A Horrocks-type theorem for even orthogonal
Andrei Lavrenov, Sergey Sinchuk
We prove the Horrocks theorem for unstable even-dimensional orthogonal Steinberg groups. The Horrocks theorem for Steinberg groups is one of the principal ingredients needed for th…
Linearity problem for non-abelian tensor products
Valeriy G. Bardakov, Andrei V. Lavrenov, Mikhail V. Neshchadim
In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor…
A local-global principle for symplectic
Andrei Lavrenov
We prove that an element of the symplectic Steinberg group is trivial if and only if its image under any maximal localisation homomorphism is trivial.
On centrality of even orthogonal
Andrei Lavrenov, Sergey Sinchuk
We give a short uniform proof of centrality of for all simply-laced root systems of rank .
Relative symplectic Steinberg group
Andrei Lavrenov
We give two definitions of relative symplectic Steinberg group and show that they coincide.
Another presentation for symplectic Steinberg groups
Andrei Lavrenov
We solve a classical problem of centrality of symplectic , namely we show that for an arbitrary commutative ring , the symplectic Steinberg group $\mathrm{…
On odd unitary Steinberg group
Andrei Lavrenov
Let be a ring with pseudo-involution, be an odd form parameter, be an odd hyperbolic unitary group, $\mathrm{EU}(2n,\,R,\,\mathf…
Linear parameterization of group GL(N, C)
A. Lavrenov
A linear parameterization of group GL(N, C) formed by direct products of matrices with in advance known symmetry properties is offered. Initial conditions of the given approach and…