*‐structures on quantum and braided spaces of the type defined via an R‐matrix are studied. These include q‐Minkowski and q‐Euclidean spaces as additive braided groups. The duality between the *‐braided groups of vectors and covectors is proved and some first applications to braided geometry are made.

1.
S. Majid, “Introduction to braided geometry and q-Minkowski space,” in Proceedings of the School on Quantum Groups, Varenna, Italy, June 1994 (to be published).
2.
S. Majid, “Beyond supersymmetry and quantum symmetry (an introduction to braided groups and braided matrices),” in Quantum Groups, Integrable Statistical Models and Knot Theory, edited by M.-L. Ge and H. J. de Vega (World Scientific, Singapore, 1993), pp. 231–282.
3.
S.
Majid
, “
Braided momentum in the q-Poincaré group
,”
J. Math. Phys.
34
,
2045
2058
(
1993
).
4.
S.
Majid
, “
Free braided differential calculus, braided binomial theorem and the braided exponential map
,”
J. Math. Phys.
34
,
4843
4856
(
1993
).
5.
A.
Kempf
and
S.
Majid
, “
Algebraic q-integration and Fourier theory on quantum and braided spaces
,”
J. Math. Phys.
35
,
6802
6837
(
1994
).
6.
S.
Majid
, “
q-epsilon tensor for quantum and braided spaces
,”
J. Math. Phys.
36
,
1991
2003
(
1994
).
7.
S.
Majid
, “
q-Euclidean space and quantum Wick rotation by twisting
,”
J. Math. Phys.
35
,
5025
5034
(
1994
).
8.
S.
Majid
, “
The quantum double as quantum mechanics
,”
J. Geom. Phys.
13
,
169
202
(
1994
).
9.
U.
Meyer
, “
q-Lorentz group and braided coaddition on q-Minkowski space
,”
Commun. Math. Phys.
168
,
249
264
(
1995
).
10.
U. Meyer, “Wave equations on q-Minkowski space,” Commun. Math. Phys. (to appear).
11.
G.
Fiore
, “
The SOq(N,R)-symmetric harmonic oscillator on the quantum Euclidean space RqN and its Hilbert space structure
,”
Int. J. Mod. Phys. A
26
,
4679
4729
(
1993
).
12.
U.
Carow-Watamura
,
M.
Schlieker
,
M.
Scholl
, and
S.
Watamura
, “
A quantum Lorentz group
,”
Int. J. Mod. Phys.
6
,
3081
3108
(
1991
).
13.
O.
Ogievetsky
,
W. B.
Schmidke
,
J.
Wess
, and
B.
Zumino
, “
q-deformed Poincaré algebra
,”
Commun. Math. Phys.
150
,
495
518
(
1992
).
14.
S.
Majid
and
U.
Meyer
, “
Braided matrix structure of q-Minkowski space and q-Poincaré group
,”
Z. Phys. C
63
,
357
362
(
1994
).
15.
S.
Majid
, “
Examples of braided groups and braided matrices
,”
J. Math. Phys.
32
,
3246
3253
(
1991
).
16.
L. D.
Faddeev
,
N. Yu.
Reshetikhin
, and
L. A.
Takhtajan
, “
Quantization of Lie groups and Lie algebras
,”
Leningrad Math J.
1
,
193
225
(
1990
).
17.
O.
Ogievetsky
and
B.
Zumino
, “
Reality in the differential calculus on q-Euclidean spaces
,”
Lett. Math. Phys.
25
,
121
130
(
1992
).
18.
A.
Kempf
, “
Quantum group-symmetric Fock-spaces and Bargmann-Fock representation
,”
Lett. Math. Phys.
26
,
1
12
(
1992
).
19.
S. L.
Woronowicz
, “
Differential calculus on compact matrix pseudogroups (quantum groups)
,”
Commun. Math. Phys.
122
,
125
170
(
1989
).
20.
J.
Wess
and
B.
Zumino
, “
Covariant differential calculus on the quantum hyperplane
,”
Proc. Supl. Nucl. Phys. B
18
,
302
(
1990
).
21.
W.
Pusz
and
S. L.
Woronowicz
, “
Twisted second quantization
,”
Rep. Math. Phys.
27
,
231
(
1989
).
22.
S. Majid, “Quasi-* structure on q-Poincaré algebras,” Damtp/95-11, 1995 (preprint).
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