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- Alexander Levichev, Olga Kosheleva
- Reliable Computing
- 1998

On August 12, 1997, Alexander Danilovich Alexandrov, the well-known geometer, a member of the Russian Academy of Sciences and of several foreign academies, will turn 85. A. D. Alexandrov’s seminal research papers cover areas ranging from quantum mechanics to geometry to philosophy of science. In particular, his innovative approach to foundations of… (More)

- A A Akopyan, A V Levichev
- 2011

We notice that there is a 2-cover P of S 1 SO(3) (we denote this group D 1/2 ) by the group U(2): P sends a matrix z into a pair (det z,v). The matrix v here is the image of u under a standard covering map p from SU(2) onto SO(3), see (3.4) below. Finally, u (being a matrix from SU(2) ) is determined (up to a sign) from the decomposition z = du, here d 2 =… (More)

The paper deals with two simply connected solvable four-dimensional Lie groups M1 and M2 . The first group is a direct product of the nilpotent Heisenberg Lie group and the one-dimensional Lie group. The second one is a direct product of the two-dimensional non-abelian Lie group and the two-dimensional abelian Lie group. Applying Methods of [4, 6] we… (More)

- A V Levichev
- 2010

Segal’s chronometry is based on a space–time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). There are exactly two more non-commutative four-dimensional Lie algebras that admit such a form. They determine space–times L and F. The world F is based on the Lie algebra u(1,1), in… (More)

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