Viktor Abramov

Prof. Dr. Viktor Abramov

Institute of Mathematics and Statistics, University of Tartu, Tartu, Tartumaa, Estonia
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Research Focus & Metrics

Academic Career Length

31Years (1996-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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1 March 1997 in Journal of Mathematical Physics
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Viktor AbramovViktor Abramov
Viktor Abramov
RKRichard Kerner
Richard Kerner
BRBertrand Le Roy
Bertrand Le Roy
We propose a generalization of non-commutative geometry and gauge theories based on ternary ℤ3-graded structures. In the new algebraic structures we define, all products of two entities are left free, the only constraining relations being imposed on ternary products. These relations reflect the action of the ℤ3-group, which may be either trivial, i.e., abc=bca=cab, generalizing the usual commutativity, or non-trivial, i.e., abc=jbca, with j=e(2πi)/3. The usual ℤ2-graded structures such as Grassmann, Lie, and Clifford algebras are generalized to the ℤ3-graded case. Certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed.

10 October 2015 in Advances in Applied Clifford Algebras
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Viktor AbramovViktor Abramov
Viktor Abramov

1 August 2000 in Journal of Mathematical Physics
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Viktor AbramovViktor Abramov
Viktor Abramov
RKR. Kerner
R. Kerner
We investigate a particular realization of generalized q-differential calculus of exterior forms on a smooth manifold based on the assumption that the N-th power (N>2) of exterior differential is equal to zero. It implies the existence of cyclic commutation relations for the differentials of first order and their generalization for the differentials of higher order. Special attention is paid to the cases N=3 and N=4. A covariant basis of the algebra of such q-grade forms is introduced, and the analogues of torsion and curvature of higher order are considered. We also study a graded exterior calculus on a generalized Clifford algebra.

1 February 1999 in Reports on Mathematical Physics
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RKRichard Kerner
Richard Kerner
Viktor AbramovViktor Abramov
Viktor Abramov

27 June 2020 in Advances in Applied Clifford Algebras
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Viktor AbramovViktor Abramov
Viktor Abramov
Sergei SilvestrovSergei Silvestrov
Sergei Silvestrov

23 October 2017 in International Journal of Geometric Methods in Modern Physics
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Viktor AbramovViktor Abramov
Viktor Abramov