TY - GEN

T1 - Gaussian noise sensitivity and Fourier tails

AU - Kindler, Guy

AU - O'Donnell, Ryan

PY - 2012

Y1 - 2012

N2 - We study the problem of matrix isomorphism of matrix Lie algebras (MatIsoLie). Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley - Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices that is closed under linear combinations and the operation [A, B] = AB - BA. Two matrix Lie algebras L, L' are matrix isomorphic if there is an invertible matrix M such that conjugating every matrix in L by M yields the set L'. We show that certain cases of MatIsoLie - for the wide and widely studied classes of semi simple and abelian Lie algebras - are equivalent to graph isomorphism and linear code equivalence, respectively. On the other hand, we give polynomial-time algorithms for other cases of MatIsoLie, which allow us to mostly derandomize a recent result of Kayal on affine equivalence of polynomials.

AB - We study the problem of matrix isomorphism of matrix Lie algebras (MatIsoLie). Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley - Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices that is closed under linear combinations and the operation [A, B] = AB - BA. Two matrix Lie algebras L, L' are matrix isomorphic if there is an invertible matrix M such that conjugating every matrix in L by M yields the set L'. We show that certain cases of MatIsoLie - for the wide and widely studied classes of semi simple and abelian Lie algebras - are equivalent to graph isomorphism and linear code equivalence, respectively. On the other hand, we give polynomial-time algorithms for other cases of MatIsoLie, which allow us to mostly derandomize a recent result of Kayal on affine equivalence of polynomials.

UR - http://www.scopus.com/inward/record.url?scp=84866494491&partnerID=8YFLogxK

U2 - 10.1109/CCC.2012.35

DO - 10.1109/CCC.2012.35

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AN - SCOPUS:84866494491

SN - 9780769547084

T3 - Proceedings of the Annual IEEE Conference on Computational Complexity

SP - 137

EP - 147

BT - Proceedings - 2012 IEEE 27th Conference on Computational Complexity, CCC 2012

T2 - IEEE Computer Society Technical Committee on Mathematical Foundations of Computing

Y2 - 26 June 2012 through 29 June 2012

ER -