Results 1 to 10 of about 8,207 (118)
Proof of some properties of transfer using noncommutative determinants [PDF]
Advances in Group Theory and Applications, 2018 A transfer is a group homomorphism from a group to an abelian quotient group of a subgroup of finite index. In this paper, we give a natural interpretation of the transfers in group theory in terms of noncommutative determinants.
Naoya Yamaguchi
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Almost settling the hardness of noncommutative determinant [PDF]
Proceedings of the forty-third annual ACM symposium on Theory of computing, 2011 20 pages, 3 ...
Chien, Steve +3 more
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On the hardness of the noncommutative determinant [PDF]
Proceedings of the forty-second ACM symposium on Theory of computing, 2010 In this paper we study the computational complexity of computing the noncommutative determinant. We first consider the arithmetic circuit complexity of computing the noncommutative determinant polynomial. Then, more generally, we also examine the complexity of computing the determinant (as a function) over noncommutative domains.
ARVIND, V, SRINIVASAN, S
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Curvature of the Determinant Line Bundle for the Noncommutative Two Torus [PDF]
Mathematical Physics, Analysis and Geometry, 2016 We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one can endow the determinant line bundle with a natural Hermitian metric.
Fathi, Ali +2 more
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Fredholm Determinants and Pole-free Solutions to the Noncommutative Painlevé II Equation [PDF]
Communications in Mathematical Physics, 2011 We extend the formalism of integrable operators a' la Its-Izergin-Korepin-Slavnov to matrix-valued convolution operators on a semi-infinite interval and to matrix integral operators with a kernel of the form E_1^T(x) E_2(y)/(x+y) thus proving that their resolvent operators can be expressed in terms of solutions of some specific Riemann-Hilbert problems.
Bertola, M., Cafasso, M.
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Wess-Zumino-Witten and fermion models in noncommutative space [PDF]
, 2000 We analyze the connection between Wess-Zumino-Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding ...
Arcioni +27 more
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Noncommutative symmetric functions and Laplace operators for classical Lie algebras [PDF]
, 1994 New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some ...
A. M. Perelomov +9 more
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A Fully Noncommutative Painlevé II Hierarchy: Lax Pair and Solutions Related to Fredholm Determinants [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 We consider Fredholm determinants of matrix Hankel operators associated to matrix versions of the n-th Airy functions. Using the theory of integrable operators, we relate them to a fully noncommutative Painlevé II hierarchy, defined through a matrix-valued version of the Lenard operators.
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Determinants as Combinatorial Summation Formulas over an Algebra with a Unique $n$-ary Operation
Известия Иркутского государственного университета: Серия "Математика", 2018 Since the late 1980s the author has published a number of results on matrix functions, which were obtained using the generating functions, mixed discriminants (mixed volumes in $\mathbb R^n$), and the well-known polarization theorem (the most general ...
G.P. Egorychev
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A Diffie-Hellman Key Exchange Using Matrices Over Non Commutative Rings [PDF]
, 2012 We consider a key exchange procedure whose security is based on the difficulty of computing discrete logarithms in a group, and where exponentiation is hidden by a conjugation. We give a platform-dependent cryptanalysis of this protocol. Finally, to take
Eftekhari, Mohammad
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