1,721,016 research outputs found
Linear ODEs: an Algebraic Perspective
Full text linkThis booklet was intended to provide a minimum of ready-to-use references for the minicourse given by the author during the XXII E ́scola de Algebra (40 Anos), held in Salvador de Bahia (July 2012). It wishes to bring to the fore a number of relationships with other branches of mathematics. Examples include the theory of symmetric functions, the theory of universal decomposition algebras associated to a polynomial, derivations of the exterior algebra of a free module, D-modules, Schubert calculus for the complex Grassmannian, boson-fermion correspondence in the representation theory of the Heisenberg algebr
Computing Gaps Sequences at Gorenstein Singularities
No full textThe paper shows on examples how to compute Weierstrass Gap Sequences at Gorenstein singularities according to the definition introduced by the author in his Doctoral Thesi
The wronskian and its derivatives
Full text linkArticolo testo di una conferenza tenuta presso l'Accademia Peloritana dei Pericolanti (Messina
Schubert Calculus via Hasse-Schmidt derivations
Full text linkA natural Hasse-Schmidt derivation on the exterior algebra of a free module realizes the (small quantum) cohomology ring of the grassmannian Gk(Cn) as a ring of operators on the exterior algebra of a free module of rank n. Classical Pieri's formula can be interpreted as Leibniz's rule enjoyed by special Schubert cycles with respect to the wedge product
Lezioni di Algebra Lineare e Geometria per l'ingegneria
No full textUn libro di testo per gli studenti del primo anno di corso
in ingegneria. Con spunti culturali
Hasse-Schmidt Derivations on Grassmann Algebras
No full textThis book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level
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