Alfredo Capelli

Alfredo Capelli (* August 5, 1855 in Milan, † January 28, 1910 in Naples) was an Italian mathematician who mainly dealt with algebra.

Capelli studied at the University of Rome, among others, Giuseppe Battaglini with the conclusion of 1877. In his thesis he proved independently by Ludwig Sylow Sylow the phrases and also later published sets of Ferdinand Georg Frobenius and William Burnside. After graduating, he worked as assistant to Felice Casorati in Pavia and studied in Berlin under Karl Weierstrass and Leopold Kronecker. In 1881 he became professor of algebraic Analysis at the University of Palermo as the successor of Cesare Arzelà. In 1886 he won the competition for the Chair of Algebra at the University of Naples.

He also established the Frattini argument in the theory of finite groups (he was friends with Giovanni Frattini and stood with him in correspondence).

In 1886 he proved ( in a book with Giovanni Garbieri ) named after him and Eugène Rouché theorem of linear algebra: Ax = b has a solution if and only if the rank of A is equal to that of the matrix (A | b). In works 1887 and 1890 he introduced the eponymous Capelli identities between differential operators in the Darstelllungstheorie of Lie algebras of significance were later ( Hermann Weyl ).

He was a member of the Accademia dei Lincei, the Academy of Sciences in Palermo, Naples and Lombardy Academy of Sciences ( Istituto Lombardo ). In 1882 he received the mathematics prize of the Accademia dei XL.

After the death of Battaglini he was editor of the Giornale di matematiche 1894.

Writings

• Sopra l' isomorfismo dei gruppi di sostituzioni, Giornale di matematiche, Volume 16, 1878, pp. 32-87
• With Giovanni Garbieri: Corso di analisi algebrica, Padua: F. sacchetto 1886
• Lezioni di algebra complementare ad uso degli Aspiranti alla licenza universitaria, Naples: Pellerano, 1895
• Istituzioni di analisi algebrica, Naples: Pellerano 1902
• Lezioni sulla teoria delle forme algebriche, Naples: Pellerano 1902