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Functional Analysis and Its Applications, 2002
Let \(P\) be an algebra of complex polynomials in \(\lambda_0, \ldots, \lambda_n\) and \(L_P\) the free left \(P\)-module with a basis \(1, l_0, \ldots, l_n\). Define the structure of a Lie algebra \(\mathfrak a(C,V)\) on \(L_P\) by setting \[ [l_i,l_j]=\sum c_{i,j}^k(\lambda)l_k,\quad [l_i,\lambda_q]=v_{i,q}(\lambda), \quad [\lambda_i,\lambda_j]=0, \]
Bukhshtaber, V. M., Leĭkin, D. V.
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Let \(P\) be an algebra of complex polynomials in \(\lambda_0, \ldots, \lambda_n\) and \(L_P\) the free left \(P\)-module with a basis \(1, l_0, \ldots, l_n\). Define the structure of a Lie algebra \(\mathfrak a(C,V)\) on \(L_P\) by setting \[ [l_i,l_j]=\sum c_{i,j}^k(\lambda)l_k,\quad [l_i,\lambda_q]=v_{i,q}(\lambda), \quad [\lambda_i,\lambda_j]=0, \]
Bukhshtaber, V. M., Leĭkin, D. V.
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On Polynomial Algebras and Free Algebras
Canadian Journal of Mathematics, 1968It is well known that given the polynomial algebra (for definitions, see §2), an algebra of type τ, and a sequence a of elements of , one can define a congruence relation θa of such that the factor algebra is isomorphic to the subalgebra of generated by a, and the isomorphism is given in a very simple way.
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Computer Algebra and Polynomials
2015Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our ...
Gutierrez, Jaime +2 more
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Polynomial algebra for Birkhoff interpolants
Numerical Algorithms, 2010The object of this paper is to use a single standard formulation to present a number of approximation formulae like those for Lagrange and Hermite-Birkhoff (HB) interpolation, divided difference, numerical quadrature and numerical differentiation. Usually stable algorithms of cost \(O(m^3) + O(p^2)\) in degree \(p\) and number \(m\) of missing data for
John C. Butcher +3 more
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HOCHSCHILD COHOMOLOGY OF POLYNOMIAL ALGEBRAS
Communications in Contemporary Mathematics, 2001In this paper we investigate the Hochschild cohomology groups H2(A) and H3(A) for an arbitrary polynomial algebra A. We also show that the corresponding cohomology groups which are built from differential operators inject in H2(A) and H3(A) and we give an application to deformation theory.
Penkava, Michael, Vanhaecke, Pol
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On Conway Algebras and the Homflypt Polynomial
Journal of Knot Theory and Its Ramifications, 1997In 1984 J. H. Przytycki and P. Traczyk introduced the notion of Conway algebras. They had proved that for every Conway algebra there exists an invariant of links in ℝ3, which takes values in that algebra. In this paper we show that any link invariant obtained in this way is not better than the Homflypt (Jones-Conway) polynomial.
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On polynomial identities in nil-algebras
Journal of Mathematical Sciences, 2007The paper under review surveys several new results concerning non-finitely based T-ideals, that is ideals of identities in the free associative algebra which do not admit any finite generating set. According to Kemer's celebrated theory every T-ideal in characteristic 0 is finitely based. On the other hand, \textit{A. Ya. Belov} [Fundam. Prikl. Mat. 5,
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Algebraic approach to univariate polynomial derivation
Georgian Mathematical Journal, 2021Ivan Pávkov
exaly
INEQUALITIES FOR ALGEBRAIC POLYNOMIALS
Mathematics of the USSR-Sbornik, 1969openaire +2 more sources