Geodesic
Zhelyabin, V.N., Kolesnikov, P.S. Dual coalgebra of the differential polinomial algebra in one variable and related coalgebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 792-803.

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that the dual coalgebra of the polynomial algebra in one variable is the space of linearly recursive sequences over an arbitrary field. Moreover, this coalgebra is a differential one relative to the dual standard derivation and does not contain nonzero finite-dimensional differentially closed subcoalgebras if the characteristic of the ground field is zero. We construct a Novikov coalgebra which is the dual coalgebra of the left-symmetric Witt algebra of index one. Also, we construct a Jordan supercoalgebra which is dual to the Jordan superalgebra of vector type of the polynomial algebra in one variable. All these coalgebras do not contain non-zero finite-dimensional subcoalgebras if the characteristic of ground field is zero. It is shown that over a field of characteristic different from 2 the adjoint Lie coalgebra of the dual coalgebra of the left-symmetric Witt algebra of index one is isomorphic to the dual coalgebra of the Witt algebra of index one.
Mots-clés : coalgebra
Keywords: coderivation, associative commutative algebra, differential algebra, Novikov algebra, Lie algebra, Witt algebra, Jordan superalgebra, locally finite coalgebra. 
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     title = {Zhelyabin, {V.N.,} {Kolesnikov,} {P.S.} {Dual} coalgebra of the differential polinomial algebra in one variable and related coalgebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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V. N. Zhelyabin; P. S. Kolesnikov. Zhelyabin, V.N., Kolesnikov, P.S. Dual coalgebra of the differential polinomial algebra in one variable and related coalgebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 792-803. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a6/

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