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  2. Modular group - Wikipedia

    en.wikipedia.org/wiki/Modular_group

    In mathematics, the modular group is the projective special linear group ⁡ (,) of 2 × 2 matrices with integer coefficients and determinant 1. The matrices A and − A are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations , and the name "modular group" comes from the relation to ...

  3. SL2 (R) - Wikipedia

    en.wikipedia.org/wiki/SL2(R)

    The braid group B 3 is the universal central extension of the modular group. Under this covering, the preimage of the modular group PSL(2, Z) is the braid group on 3 generators, B 3, which is the universal central extension of the modular group. These are lattices inside the relevant algebraic groups, and this corresponds algebraically to the ...

  4. Modular invariant theory - Wikipedia

    en.wikipedia.org/wiki/Modular_invariant_theory

    In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by Dickson (2004) .

  5. Mapping class group of a surface - Wikipedia

    en.wikipedia.org/wiki/Mapping_class_group_of_a...

    In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topology) deformation.

  6. j-invariant - Wikipedia

    en.wikipedia.org/wiki/J-invariant

    Thus their quotient, and therefore j, is a modular function of weight zero, in particular a holomorphic function H → C invariant under the action of SL(2, Z). Quotienting out by its centre { ±I } yields the modular group, which we may identify with the projective special linear group PSL(2, Z).

  7. Modular curve - Wikipedia

    en.wikipedia.org/wiki/Modular_curve

    The modular group SL(2, Z) acts on the upper half-plane by fractional linear transformations.The analytic definition of a modular curve involves a choice of a congruence subgroup Γ of SL(2, Z), i.e. a subgroup containing the principal congruence subgroup of level N for some positive integer N, which is defined to be

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    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. Analog Devices - Wikipedia

    en.wikipedia.org/wiki/Analog_Devices

    The company was founded by two MIT graduates, Ray Stata and Matthew Lorber in 1965. [9] The same year, the company released its first product, the model 101 op amp, [10] which was a hockey-puck sized module used in test and measurement equipment. [11] In 1967, the company published the first issue of its technical magazine, Analog Dialogue. [12]

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