Erlangen Programme At Large Sl

1. Variety of different geometries. 2. Riemann vs Klein approaches. 3. Covariance of physical theories. 4.

1.

1. Integral transforms from induced wavelet transforms. 2. Cauchy-Riemann operator 3. Hyperbolic integral transform, wave ...

1. Cartesian and

1. Rotations of unit disk and orthogonality of lines revisited. 2. Moebius transformations, cycles and FSCc matrices in higher ...

1. A group action and its orbits, homogeneous spaces. 2. A homogeneous space and isotropy subgroups. 3. A subgroup H and ...

1. Unification of elliptic/parabolic/hyperbolic cases 2. Invariance of cycles 3. Divisors of zero and compactifications of plane 4.

1. Geometric characters of subgroup N 2. Tropical mathematics 3. Representations of

1. Divisors of zero and ideal elements of the projective spaces. 2. Cycles as points of a projective space, independent ...

1. Linear and quadratic pencils of cycles. 2. Distance, length, and conformality. 3. Isometric action of

1. Homogeneous coordinates and the projective real line. 2. Moebius transformations as maps of the projective real line.

1. Cayley transform, the group SU(1,1) and the unit disk in C. 2. Iwasawa

1. Review of Moebius transformations, FLT relations. 2. Review of Poincare extensions, loxodromes, continued fractions, discrete ...

1. Classification of all 2-dim continuous subgroups--subgroup F of upper triangular matrices. 2. Any continuous 1-parameter ...

1. Orthogonality of cycles revisited 2. Orthogonality and incidence 3. Orthogonality of pencils 4. Orthogonality and inversion: ...

1. Poincare unit disk, Cayley transform 2. Hypercomplex unit disk 3. Space-time geomtry, red shift and future/past separation 4.

1. Mysterious connections between geometric and algebraic invariants 2. Indefinite inner product and Cauchy-Schwarz inequality ...

1. Complex, dual and double numbers 2. Iwasawa decomposition