As K. Nomizu has justly noted [K. Nomizu, 56], Differential Geometry ever will be initiating newer and newer aspects of the theory of Lie groups. This monograph is devoted to just some such aspects of Lie groups and Lie algebras. New differential geometric problems came into being in connection with so called subsymmetric spaces, subsymmetries, and mirrors introduced in our works dating back to 1957 [L.V. Sabinin, 58a,59a,59b]. In addition, the exploration of mirrors and systems of mirrors is of interest in the case of symmetric spaces. Geometrically, the most rich in content there appeared to be the homogeneous Riemannian spaces with systems of mirrors generated by commuting subsymmetries, in particular, so called tri-symmetric spaces introduced in [L.V. Sabinin, 61b]. As to the concrete geometric problem which needs be solved and which is solved in this monograph, we indicate, for example, the problem of the classification of all tri-symmetric spaces with simple compact groups of motions. Passing from groups and subgroups connected with mirrors and subsymmetries to the corresponding Lie algebras and subalgebras leads to an important new concept of the involutive sum of Lie algebras [L.V. Sabinin, 65]. This concept is directly concerned with unitary symmetry of elementary par- cles (see [L.V. Sabinin, 95,85] and Appendix 1). The first examples of involutive (even iso-involutive) sums appeared in the - ploration of homogeneous Riemannian spaces with and axial symmetry. The consideration of spaces with mirrors [L.V. Sabinin, 59b] again led to iso-involutive sums.

*"synopsis" may belong to another edition of this title.*

Published by
Springer
(2004)

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Springer, 2004. Condition: New. book. Seller Inventory # M1402025440

Published by
Springer
(2004)

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Springer, 2004. Hardcover. Condition: New. 2004. Seller Inventory # DADAX1402025440

Published by
Springer
(2004)

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Springer, 2004. Hardback. Condition: NEW. 9781402025440 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Seller Inventory # HTANDREE0289460

Published by
Springer
(2016)

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Paperback
Quantity Available: 1

Seller:

Rating

**Book Description **Springer, 2016. Paperback. Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Seller Inventory # ria9781402025440_lsuk

Published by
Springer-Verlag New York Inc., United States
(2004)

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Springer-Verlag New York Inc., United States, 2004. Hardback. Condition: New. 2004 ed.. Language: English . Brand New Book ***** Print on Demand *****.As K. Nomizu has justly noted [K. Nomizu, 56], Differential Geometry ever will be initiating newer and newer aspects of the theory of Lie groups. This monograph is devoted to just some such aspects of Lie groups and Lie algebras. New differential geometric problems came into being in connection with so called subsymmetric spaces, subsymmetries, and mirrors introduced in our works dating back to 1957 [L.V. Sabinin, 58a,59a,59b]. In addition, the exploration of mirrors and systems of mirrors is of interest in the case of symmetric spaces. Geometrically, the most rich in content there appeared to be the homogeneous Riemannian spaces with systems of mirrors generated by commuting subsymmetries, in particular, so called tri-symmetric spaces introduced in [L.V. Sabinin, 61b]. As to the concrete geometric problem which needs be solved and which is solved in this monograph, we indicate, for example, the problem of the classification of all tri-symmetric spaces with simple compact groups of motions. Passing from groups and subgroups connected with mirrors and subsymmetries to the corresponding Lie algebras and subalgebras leads to an important new concept of the involutive sum of Lie algebras [L.V. Sabinin, 65]. This concept is directly concerned with unitary symmetry of elementary par- cles (see [L.V. Sabinin, 95,85] and Appendix 1). The first examples of involutive (even iso-involutive) sums appeared in the - ploration of homogeneous Riemannian spaces with and axial symmetry. The consideration of spaces with mirrors [L.V. Sabinin, 59b] again led to iso-involutive sums. Seller Inventory # APC9781402025440

Published by
Springer
(2004)

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Springer, 2004. Hardcover. Condition: New. This item is printed on demand. Seller Inventory # INGM9781402025440

Published by
Springer-Verlag New York Inc., United States
(2004)

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Springer-Verlag New York Inc., United States, 2004. Hardback. Condition: New. 2004 ed.. Language: English . Brand New Book ***** Print on Demand *****. As K. Nomizu has justly noted [K. Nomizu, 56], Differential Geometry ever will be initiating newer and newer aspects of the theory of Lie groups. This monograph is devoted to just some such aspects of Lie groups and Lie algebras. New differential geometric problems came into being in connection with so called subsymmetric spaces, subsymmetries, and mirrors introduced in our works dating back to 1957 [L.V. Sabinin, 58a,59a,59b]. In addition, the exploration of mirrors and systems of mirrors is of interest in the case of symmetric spaces. Geometrically, the most rich in content there appeared to be the homogeneous Riemannian spaces with systems of mirrors generated by commuting subsymmetries, in particular, so called tri-symmetric spaces introduced in [L.V. Sabinin, 61b]. As to the concrete geometric problem which needs be solved and which is solved in this monograph, we indicate, for example, the problem of the classification of all tri-symmetric spaces with simple compact groups of motions. Passing from groups and subgroups connected with mirrors and subsymmetries to the corresponding Lie algebras and subalgebras leads to an important new concept of the involutive sum of Lie algebras [L.V. Sabinin, 65]. This concept is directly concerned with unitary symmetry of elementary par- cles (see [L.V. Sabinin, 95,85] and Appendix 1). The first examples of involutive (even iso-involutive) sums appeared in the - ploration of homogeneous Riemannian spaces with and axial symmetry. The consideration of spaces with mirrors [L.V. Sabinin, 59b] again led to iso-involutive sums. Seller Inventory # APC9781402025440

Published by
Springer

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: > 20

Seller:

Rating

**Book Description **Springer. Hardcover. Condition: New. 1402025440 Special order direct from the distributor. Seller Inventory # ING9781402025440

Published by
Springer

ISBN 10: 1402025440
ISBN 13: 9781402025440

New
Hardcover
Quantity Available: > 20

Seller:

Rating

**Book Description **Springer. Hardcover. Condition: New. 312 pages. Dimensions: 9.4in. x 6.2in. x 0.9in.This book describes a new and original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. Special systems of mirrors are used for classification purposes and as an instrument for studies of Homogeneous spaces. Tri-symmetric and arbitrary Riemannian Homogeneous spaces can also be researched in this way. The book should be of particular interest to researchers in Lie Groups, Lie Algebras, Differential Geometry and their applications but it should also prove useful for other postgraduate and advanced graduate students in mathematics. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Seller Inventory # 9781402025440