Am I wasting half my disk space by not mounting a volume?

I inherited a Debian server from the previous sysadmin who left, without much documentation. I'm not a sysadmin, but I guess for now I'll have to be, and I'm trying to understand what disks and volumes/partitions there are on these machines, but LVM is new to me.

My question: Is this "shared" volume group being wasted? If df doesn't list it mounted anywhere, does that mean it's not being used?

Here is some output from commands that I know or googled:

Disk space usage:

root@server1:/$ df -hlT
Filesystem    Type    Size  Used Avail Use% Mounted on
/dev/xvda1     xfs     19G  2.2G   17G  12% /
tmpfs        tmpfs    2.0G     0  2.0G   0% /lib/init/rw
udev         tmpfs    2.0G  100K  2.0G   1% /dev
tmpfs        tmpfs    2.0G  4.0K  2.0G   1% /dev/shm
/dev/mapper/storage-a
           xfs    129G   74G   56G  57% /var

fdisk

root@server1:/$ fdisk -l

Disk /dev/xvda: 21.5 GB, 21474836480 bytes
255 heads, 63 sectors/track, 2610 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x00000000

    Device Boot      Start         End      Blocks   Id  System
/dev/xvda1               1        2432    19530752   83  Linux
/dev/xvda2            2432        2611     1438720   82  Linux swap / Solaris

Disk /dev/xvdb: 247.0 GB, 246960619520 bytes
255 heads, 63 sectors/track, 30024 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x404c04a6

    Device Boot      Start         End      Blocks   Id  System
/dev/xvdb1               1       13055   104864256   8e  Linux LVM
/dev/xvdb2           13056       30024   136303492+  8e  Linux LVM

Disk /dev/dm-0: 138.4 GB, 138412032000 bytes
255 heads, 63 sectors/track, 16827 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x00000000

Disk /dev/dm-0 doesn't contain a valid partition table

Disk /dev/dm-1: 104.9 GB, 104857600000 bytes
255 heads, 63 sectors/track, 12748 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x00000000

Disk /dev/dm-1 doesn't contain a valid partition table

Various displays:

root@server1:/$ vgdisplay -C
  VG      #PV #LV #SN Attr   VSize   VFree
  shared    1   1   0 wz--n- 100.00g 2.35g
  storage   1   1   0 wz--n- 129.99g 1.08g
root@server1:/$ lvdisplay -C
  LV   VG      Attr   LSize   Origin Snap%  Move Log Copy%  Convert
  a    shared  -wi-a-  97.66g                                      
  a    storage -wi-ao 128.91g                                      
root@server1:/$ pvdisplay -C
  PV         VG      Fmt  Attr PSize   PFree
  /dev/xvdb1 shared  lvm2 a-   100.00g 2.35g
  /dev/xvdb2 storage lvm2 a-   129.99g 1.08g
root@server1:/$ dmsetup ls
shared-a    (254, 1)
storage-a   (254, 0)

So I think I see two "physical" disks, /dev/xvda with ~20 GB and /dev/xvdb with ~250 GB.

The bigger disk seems to consist of two LVM volumes, /dev/xvdb1 (or should I call it /dev/dm-1) has about ~100 GB, and /dev/xvdb2 (or should I call it /dev/dm-0) has about ~130 GB.

The bigger logical volume group seems to be called "storage", whereas the smaller lvg is called "shared".

I'll repeat my question: Is this "shared" volume group being wasted? If df doesn't list it mounted anywhere, does that mean it's not being used?

EDIT: added output of dmsetup ls per request.