Zobrazeno 1 - 10
of 102
pro vyhledávání: '"Gatto, Letterio"'
Autor:
Gatto, Letterio, Yousofzadeh, Malihe
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of this paper i
Externí odkaz:
http://arxiv.org/abs/2410.15152
Autor:
Gatto, Letterio, Rowen, Louis
Publikováno v:
Communications in Mathematics, Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024") (January 3, 2024) cm:12413
Extending the theory of systems, we introduce a theory of Lie semialgebra ``pairs'' which parallels the classical theory of Lie algebras, but with a ``null set'' replacing $0$. A selection of examples is given. These Lie pairs comprise two categories
Externí odkaz:
http://arxiv.org/abs/2309.03867
We introduce a theory of Clifford semialgebra systems, with application to representation theory via Hasse-Schmidt derivations on exterior semialgebras. Our main result, after the construction of the Clifford semialgebra, is a formula describing the
Externí odkaz:
http://arxiv.org/abs/2108.03617
Autor:
Gatto, Letterio
The polynomial ring $B$ in infinitely many indeterminates $(x_1,x_2,\ldots)$, with rational coefficients, has a vector space basis of Schur polynomials, parametrized by partitions. The goal of this note is to provide an explanation of the following f
Externí odkaz:
http://arxiv.org/abs/2107.06938
Autor:
Behzad, Ommolbanin, Gatto, Letterio
We describe the fermionic and bosonic Fock representation of the Lie super-algebra of endomorphisms of the exterior algebra of the ${\mathbb Q}$-vector space of infinite countable dimension, vanishing at all but finitely many basis elements. We achie
Externí odkaz:
http://arxiv.org/abs/2009.00479
A polynomial ring with rational coefficients is an irreducible representation of Lie algebras of endomorphisms of exterior powers of a infinite countable dimensional $\mathbb{Q}$-vector space. We give an explicit description of it, using suitable ver
Externí odkaz:
http://arxiv.org/abs/2005.01154
Autor:
Gatto, Letterio, Salehyan, Parham
The integral singular cohomology ring of the Grassmann variety parametrizing $r$-dimensional subspaces in the $n$-dimensional complex vector space is naturally an irreducible representation of the Lie algebra of all the $n\times n$ matrices with inte
Externí odkaz:
http://arxiv.org/abs/1902.03824
Autor:
Gatto, Letterio, Salehyan, Parham
The {\em Schubert derivation} is a distinguished Hasse-Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the Schubert
Externí odkaz:
http://arxiv.org/abs/1901.06853
Autor:
Gatto, Letterio, Scherbak, Inna
Using the natural notion of {\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, "{\em each endomorphism of a finite
Externí odkaz:
http://arxiv.org/abs/1901.02686